一个三位数 [abc]，减去它的各位数码之和 a+b+c，得到一个三位数 [6x6]，求其中的 x

王守恩

我们称这串数{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, ......为潇洒数。

特别地我们把十位数字 = 0 的取出来。则

{1, 99999999909},——第1个数 = 99999999909。
{2, 999999999909},——第2个数 = 999999999909。
{3, 9999999999909},——第3个数 = 9999999999909。
{4, 99999999999909},
{5, 999999999999909},
{6, 9999999999999909},
{7, 99999999999999909},
{8, 999999999999999909},
{9, 9999999999999999909},

王守恩

我们称这串数{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, ......为潇洒数。

潇洒！——自由奔放！——不可以——不可以写成“任意数 - 数码和的差”！——潇洒地游离在规则之外——无拘无束！——潇洒走一回！

潇洒数——可以分成A,B两类——也是只能分成A,B两类。连续2个数的差=9,我们称较大的那个数为A。连续2个数的差=99,我们称较大的那个数为B。

3位潇洒数有10个=1(A)+9(B)。
4位潇洒数有100个=10(A)+90(B)。
5位潇洒数有1000个=100(A)+900(B)。
6位潇洒数有10000个=1000(A)+9000(B)。
6位潇洒数有100000个=10000(A)+90000(B)。
......
B虽然很多——规律明显——就是连续10个B抱团——永远不变。

A数量不多——潇洒!——可以连续n个抱团——n=1, 2, 3, 4 ,5, 6, 7, 8, 9, .....潇洒！
连续1个。9=990-981。
连续2个。9=9990-9981=9981-9972。
连续3个。9=99990-99981=99981-99972=99972-99963。
连续4个。9=999990-999981=999981-999972=999972-999963=999963-999954。
连续5个。9=9999990-9999981=9999981-9999972=9999972-9999963=9999963-9999954=9999954-9999945。
......
得到一串数——{981, 9972, 99963, 999954, 9999945, 99999936, 999999927, 9999999918, 99999999909, 999999999900, 9999999999891, 99999999999882, 999999999999873, 9999999999999864}——最小的。

Table[10^n - 9 n + 8, {n, 3, 16}]

王守恩

简化一下。——B永远只有10个。A在慢慢长大——潇洒!

0090, 0189, 0288, 0387, 0486, 0585, 0684, 0783, 0882, 0981, 0990,
1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 1989,
2088, 2187, 2286, 2385, 2484, 2583, 2682, 2781, 2880, 2979, 2988,
3087, 3186, 3285, 3384, 3483, 3582, 3681, 3780, 3879, 3978, 3987,
4086, 4185, 4284, 4383, 4482, 4581, 4680, 4779, 4878, 4977, 4986,
5085, 5184, 5283, 5382, 5481, 5580, 5679, 5778, 5877, 5976, 5985,
6084, 6183, 6282, 6381, 6480, 6579, 6678, 6777, 6876, 6975, 6984,
7083, 7182, 7281, 7380, 7479, 7578, 7677, 7776, 7875, 7974, 7983,
8082, 8181, 8280, 8379, 8478, 8577, 8676, 8775, 8874, 8973, 8982,

09081, 09180, 09279, 09378, 09477, 09576, 09675, 09774, 09873, 09972, 09981, 09990,
19080, 19179, 19278, 19377, 19476, 19575, 19674, 19773, 19872, 19971, 19980, 19989,
29079, 29178, 29277, 29376, 29475, 29574, 29673, 29772, 29871, 29970, 29979, 29988,
39078, 39177, 39276, 39375, 39474, 39573, 39672, 39771, 39870, 39969, 39978, 39987,
49077, 49176, 49275, 49374, 49473, 49572, 49671, 49770, 49869, 49968, 49977, 49986,
59076, 59175, 59274, 59373, 59472, 59571, 59670, 59769, 59868, 59967, 59976, 59985,
69075, 69174, 69273, 69372, 69471, 69570, 69669, 69768, 69867, 69966, 69975, 69984,
79074, 79173, 79272, 79371, 79470, 79569, 79668, 79767, 79866, 79965, 79974, 79983,
89073, 89172, 89271, 89370, 89469, 89568, 89667, 89766, 89865, 89964, 89973, 89982,

099072, 099171, 099270, 099369, 099468, 099567, 099666, 099765, 099864, 099963, 099972, 099981, 099990,
199071, 199170, 199269, 199368, 199467, 199566, 199665, 199764, 199863, 199962, 199971, 199980, 199989,
299070, 299169, 299268, 299367, 299466, 299565, 299664, 299763, 299862, 299961, 299970, 299979, 299988,
399069, 399168, 399267, 399366, 399465, 399564, 399663, 399762, 399861, 399960, 399969, 399978, 399987,
499068, 499167, 499266, 499365, 499464, 499563, 499662, 499761, 499860, 499959, 499968, 499977, 499986,
599067, 599166, 599265, 599364, 599463, 599562, 599661, 599760, 599859, 599958, 599967, 599976, 599985,
699066, 699165, 699264, 699363, 699462, 699561, 699660, 699759, 699858, 699957, 699966, 699975, 699984,
799065, 799164, 799263, 799362, 799461, 799560, 799659, 799758, 799857, 799956, 799965, 799974, 799983,
899064, 899163, 899262, 899361, 899460, 899559, 899658, 899757, 899856, 899955, 899964, 899973, 899982,

{0999063, 0999162, 0999261, 0999360, 0999459, 0999558, 0999657, 0999756, 0999855, 0999954, 0999963, 0999972, 0999981, 0999990},
{1999062, 1999161, 1999260, 1999359, 1999458, 1999557, 1999656, 1999755, 1999854, 1999953, 1999962, 1999971, 1999980, 1999989},
{2999061, 2999160, 2999259, 2999358, 2999457, 2999556, 2999655, 2999754, 2999853, 2999952, 2999961, 2999970, 2999979, 2999988},
{3999060, 3999159, 3999258, 3999357, 3999456, 3999555, 3999654, 3999753, 3999852, 3999951, 3999960, 3999969, 3999978, 3999987},
{4999059, 4999158, 4999257, 4999356, 4999455, 4999554, 4999653, 4999752, 4999851, 4999950, 4999959, 4999968, 4999977, 4999986},
{5999058, 5999157, 5999256, 5999355, 5999454, 5999553, 5999652, 5999751, 5999850, 5999949, 5999958, 5999967, 5999976, 5999985},
{6999057, 6999156, 6999255, 6999354, 6999453, 6999552, 6999651, 6999750, 6999849, 6999948, 6999957, 6999966, 6999975, 6999984},
{7999056, 7999155, 7999254, 7999353, 7999452, 7999551, 7999650, 7999749, 7999848, 7999947, 7999956, 7999965, 7999974, 7999983},
{8999055, 8999154, 8999253, 8999352, 8999451, 8999550, 8999649, 8999748, 8999847, 8999946, 8999955, 8999964, 8999973, 8999982}}

{09999054, 09999153, 09999252, 09999351, 09999450, 09999549, 09999648, 09999747, 09999846, 09999945, 09999954, 09999963, 09999972, 09999981, 09999990},
{19999053, 19999152, 19999251, 19999350, 19999449, 19999548, 19999647, 19999746, 19999845, 19999944, 19999953, 19999962, 19999971, 19999980, 19999989},
{29999052, 29999151, 29999250, 29999349, 29999448, 29999547, 29999646, 29999745, 29999844, 29999943, 29999952, 29999961, 29999970, 29999979, 29999988},
{39999051, 39999150, 39999249, 39999348, 39999447, 39999546, 39999645, 39999744, 39999843, 39999942, 39999951, 39999960, 39999969, 39999978, 39999987},
{49999050, 49999149, 49999248, 49999347, 49999446, 49999545, 49999644, 49999743, 49999842, 49999941, 49999950, 49999959, 49999968, 49999977, 49999986},
{59999049, 59999148, 59999247, 59999346, 59999445, 59999544, 59999643, 59999742, 59999841, 59999940, 59999949, 59999958, 59999967, 59999976, 59999985},
{69999048, 69999147, 69999246, 69999345, 69999444, 69999543, 69999642, 69999741, 69999840, 69999939, 69999948, 69999957, 69999966, 69999975, 69999984},
{79999047, 79999146, 79999245, 79999344, 79999443, 79999542, 79999641, 79999740, 79999839, 79999938, 79999947, 79999956, 79999965, 79999974, 79999983},
{89999046, 89999145, 89999244, 89999343, 89999442, 89999541, 89999640, 89999739, 89999838, 89999937, 89999946, 89999955, 89999964, 89999973, 89999982}}

{099999045, 099999144, 099999243, 099999342, 099999441, 099999540, 099999639, 099999738, 099999837, 099999936, 099999945, 099999954, 099999963, 099999972, 099999981, 099999990},
{199999044, 199999143, 199999242, 199999341, 199999440, 199999539, 199999638, 199999737, 199999836, 199999935, 199999944, 199999953, 199999962, 199999971, 199999980, 199999989},
{299999043, 299999142, 299999241, 299999340, 299999439, 299999538, 299999637, 299999736, 299999835, 299999934, 299999943, 299999952, 299999961, 299999970, 299999979, 299999988},
{399999042, 399999141, 399999240, 399999339, 399999438, 399999537, 399999636, 399999735, 399999834, 399999933, 399999942, 399999951, 399999960, 399999969, 399999978, 399999987},
{499999041, 499999140, 499999239, 499999338, 499999437, 499999536, 499999635, 499999734, 499999833, 499999932, 499999941, 499999950, 499999959, 499999968, 499999977, 499999986},
{599999040, 599999139, 599999238, 599999337, 599999436, 599999535, 599999634, 599999733, 599999832, 599999931, 599999940, 599999949, 599999958, 599999967, 599999976, 599999985},
{699999039, 699999138, 699999237, 699999336, 699999435, 699999534, 699999633, 699999732, 699999831, 699999930, 699999939, 699999948, 699999957, 699999966, 699999975, 699999984},
{799999038, 799999137, 799999236, 799999335, 799999434, 799999533, 799999632, 799999731, 799999830, 799999929, 799999938, 799999947, 799999956, 799999965, 799999974, 799999983},
{899999037, 899999136, 899999235, 899999334, 899999433, 899999532, 899999631, 899999730, 899999829, 899999928, 899999937, 899999946, 899999955, 899999964, 899999973, 899999982}}

{0999999036, 0999999135, 0999999234, 0999999333, 0999999432, 0999999531, 0999999630, 0999999729, 0999999828, 0999999927, 0999999936, 0999999945, 0999999954, 0999999963, 0999999972, 0999999981, 0999999990},
{1999999035, 1999999134, 1999999233, 1999999332, 1999999431, 1999999530, 1999999629, 1999999728, 1999999827, 1999999926, 1999999935, 1999999944, 1999999953, 1999999962, 1999999971, 1999999980, 1999999989},
{2999999034, 2999999133, 2999999232, 2999999331, 2999999430, 2999999529, 2999999628, 2999999727, 2999999826, 2999999925, 2999999934, 2999999943, 2999999952, 2999999961, 2999999970, 2999999979, 2999999988},
{3999999033, 3999999132, 3999999231, 3999999330, 3999999429, 3999999528, 3999999627, 3999999726, 3999999825, 3999999924, 3999999933, 3999999942, 3999999951, 3999999960, 3999999969, 3999999978, 3999999987},
{4999999032, 4999999131, 4999999230, 4999999329, 4999999428, 4999999527, 4999999626, 4999999725, 4999999824, 4999999923, 4999999932, 4999999941, 4999999950, 4999999959, 4999999968, 4999999977, 4999999986},
{5999999031, 5999999130, 5999999229, 5999999328, 5999999427, 5999999526, 5999999625, 5999999724, 5999999823, 5999999922, 5999999931, 5999999940, 5999999949, 5999999958, 5999999967, 5999999976, 5999999985},
{6999999030, 6999999129, 6999999228, 6999999327, 6999999426, 6999999525, 6999999624, 6999999723, 6999999822, 6999999921, 6999999930, 6999999939, 6999999948, 6999999957, 6999999966, 6999999975, 6999999984},
{7999999029, 7999999128, 7999999227, 7999999326, 7999999425, 7999999524, 7999999623, 7999999722, 7999999821, 7999999920, 7999999929, 7999999938, 7999999947, 7999999956, 7999999965, 7999999974, 7999999983},
{8999999028, 8999999127, 8999999226, 8999999325, 8999999424, 8999999523, 8999999622, 8999999721, 8999999820, 8999999919, 8999999928, 8999999937, 8999999946, 8999999955, 8999999964, 8999999973, 8999999982}}

W[k_] := Table[10^(k + 2) - 9 k - 901 + i (10^(k + 2) - 1) + If[j < 10, 99 j, 9 j + 810], {i, 0, 8}, {j, 0, k + 9}]; W[7]

王守恩

我们称这串数{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, ......为潇洒数。

潇洒数就应该配潇洒公式！——潇洒来一个！

Complement[Range[9, 999999, 9], Table[10 n - Tr[IntegerDigits[n]], {n, 999999}]]——潇洒公式

A282473——Multiples of 9 which cannot be expressed as the difference between a natural number k and its digit sum s(k).

90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 1989, 2088, 2187, 2286, 2385, 2484, 2583, 2682, 2781, 2880, 2979, 2988, 3087, 3186, 3285, 3384, 3483, 3582, 3681, 3780, 3879,

COMMENTS——Based on empirical observations, it can be noted that the difference between consecutive terms is usually 99. However, this breaks down when the hundreds digit is 9,
in which case the difference between consecutive terms is 9. This changes back, however.——想错啦！

LINKS——Charles R Greathouse IV, Table of n, a(n) for n = 1..10000——这里只有10000——潇洒公式可以足够大！

Brilliant.org, Those are some nifty numbers——Australian Mathematics Olympiad, Question 2, 2015, p. 84.

EXAMPLE——If k=90, then k-s(k)=81. If k=100, then k-s(k)=99. This is an increasing function, so k-s(k)=90 is unachievable.

MATHEMATICA

okQ[n_] := Catch[ Do[ If[ x- Total@ IntegerDigits@ x == n, Throw@ False], {x, n, n+ 9 IntegerLength[n]}]; True]; Select[9 Range[1000], okQ[#] &]——没有潇洒公式好。

(* Giovanni Resta, Feb 27 2017 *)

我还是那句话——我们不是AI的奴隶——AI是我们的工具——潇洒公式——AI是想不出来的！

王守恩

楼上的公式废了！——这个才叫公式！！——那速度不是一般的快！！！

Flatten[Table[100 n - Tr[IntegerDigits[n]] - 9 Reverse[Range[IntegerExponent[n, 10] + 1]], {n, 90}]]
{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 1989, 2088, 2187, 2286, 2385, 2484, 2583, 2682, 2781, 2880, 2979, 2988, 3087, 3186,
3285, 3384, 3483, 3582, 3681, 3780, 3879, 3978, 3987, 4086, 4185, 4284, 4383, 4482, 4581, 4680, 4779, 4878, 4977, 4986, 5085, 5184, 5283, 5382, 5481, 5580, 5679, 5778, 5877, 5976, 5985, 6084, 6183,
6282, 6381, 6480, 6579, 6678, 6777, 6876, 6975, 6984, 7083, 7182, 7281, 7380, 7479, 7578, 7677, 7776, 7875, 7974, 7983, 8082, 8181, 8280, 8379, 8478, 8577, 8676, 8775, 8874, 8973, 8982}

“满纸荒唐言，一把辛酸泪。都云作者痴，谁解其中味？”——分享快乐！！！

王守恩

我们称这串数{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, ......为潇洒数。

潇洒！——不可以——不可以写成 “任意数 - 数码和的差” ——潇洒地游离在规则之外——无拘无束！

潇洒数——可以分成 A,B 两类。A = 9 = 连续 2 个数的差。B = 99 = 连续 2 个数的差。

B——永远是连续 10 个 B 抱团。

A——可以是连续 n 个抱团——n = 1, 2, 3, 4 ,5, 6, 7, 8, 9, ......——譬如连续 100个 抱团——潇洒走一回！

  {99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999099,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999108,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999117,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999126,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999135,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999144,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999153,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999162,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999171,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999180,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999189,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999198,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999207,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999216,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999225,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999234,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999243,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999252,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999261,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999270,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999279,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999288,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999297,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999306,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999315,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999324,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999333,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999342,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999351,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999360,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999369,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999378,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999387,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999396,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999405,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999414,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999423,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999432,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999441,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999450,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999459,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999468,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999477,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999486,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999495,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999504,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999513,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999522,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999531,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999540,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999549,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999558,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999567,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999576,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999585,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999594,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999603,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999612,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999621,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999630,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999639,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999648,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999657,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999675,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999684,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999693,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999702,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999711,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999720,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999729,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999738,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999747,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999756,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999765,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999774,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999783,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999792,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999801,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999810,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999819,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999828,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999837,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999846,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999855,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999864,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999873,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999882,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999891,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999909,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999918,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999927,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999936,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999945,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999954,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999963,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999972,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999981,
   99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990}

王守恩

楼上的公式废了！——这个才叫公式！！——那速度不是一般的快！！！——没有重复！没有遗漏！无需排序！——一气呵成！

Table[100 n - Tr[IntegerDigits[n]] - 9 Reverse[Range[IntegerExponent[10n, 10]]], {n, 90}]
{90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 1989, 2088, 2187, 2286, 2385, 2484, 2583, 2682, 2781, 2880, 2979, 2988, 3087, 3186,
3285, 3384, 3483, 3582, 3681, 3780, 3879, 3978, 3987, 4086, 4185, 4284, 4383, 4482, 4581, 4680, 4779, 4878, 4977, 4986, 5085, 5184, 5283, 5382, 5481, 5580, 5679, 5778, 5877, 5976, 5985, 6084, 6183,
6282, 6381, 6480, 6579, 6678, 6777, 6876, 6975, 6984, 7083, 7182, 7281, 7380, 7479, 7578, 7677, 7776, 7875, 7974, 7983, 8082, 8181, 8280, 8379, 8478, 8577, 8676, 8775, 8874, 8973, 8982}

关键是3点——1,100 n = 100 n。2,Tr[IntegerDigits[n]] = S(n)。3, 9 Range[IntegerExponent[10n, 10]] = 9 k。
k = 1, 是 B 类 = 固定连续 10 个抱团。k > 1, 是 A 类。A类不固定, 可以是连续任意个抱团。

看看——A282473——把简单问题想复杂了！
Multiples of 9 which cannot be expressed as the difference between a natural number k and its digit sum s(k).

90, 189, 288, 387, 486, 585, 684, 783, 882, 981, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 1989, 2088, 2187, 2286, 2385, 2484, 2583, 2682, 2781, 2880, 2979, 2988, 3087, 3186, 3285, 3384, 3483, 3582, 3681, 3780,

COMMENTS——Based on empirical observations, it can be noted that the difference between consecutive terms is usually 99. However,
this breaks down when the hundreds digit is 9, in which case the difference between consecutive terms is 9. This changes back, however.——想复杂了！
LINKS——Charles R Greathouse IV, Table of n, a(n) for n = 1..10000——
Brilliant.org, Those are some nifty numbers——Australian Mathematics Olympiad, Question 2, 2015, p. 84.
EXAMPLE——If k=90, then k-s(k)=81. If k=100, then k-s(k)=99. This is an increasing function, so k-s(k)=90 is unachievable.——错啦！
MATHEMATICA——okQ[n_] := Catch[ Do[ If[ x- Total@ IntegerDigits@ x == n, Throw@ False], {x, n, n+ 9 IntegerLength[n]}]; True]; Select[9 Range[1000], okQ[#] &] (* Giovanni Resta, Feb 27 2017 *)

王守恩

想明白了——潇洒数字串也就是个等差数字串——前10000项与OEISA282473一模一样！

Transpose[{Range@Length@#, #}] &[Join @@ Table[100 n - Tr@IntegerDigits[n] - 9 Range[IntegerExponent[10 n, 10], 1, -1], {n, 9001}]]——潇洒的公式。

{{1, 90}, {2, 189}, {3, 288}, {4, 387}, {5, 486}, {6, 585}, {7, 684}, {8, 783}, {9, 882}, {10, 981}, {11, 990}, {12, 1089}, {13, 1188}, {14, 1287}, {15, 1386}, {16, 1485}, {17, 1584}, {18, 1683}, {19, 1782}, {20, 1881}, {21, 1980},
{22, 1989}, {23, 2088}, {24, 2187}, {25, 2286}, {26, 2385}, {27, 2484}, {28, 2583}, {29, 2682}, {30, 2781}, {31, 2880}, {32, 2979}, {33, 2988}, {34, 3087}, {35, 3186}, {36, 3285}, {37, 3384}, {38, 3483}, {39, 3582}, {40, 3681},
{41, 3780}, {42, 3879}, {43, 3978}, {44, 3987}, {45, 4086}, {46, 4185}, {47, 4284}, {48, 4383}, {49, 4482}, {50, 4581}, {51, 4680}, {52, 4779}, {53, 4878}, {54, 4977}, {55, 4986}, {56, 5085}, {57, 5184}, {58, 5283}, {59, 5382},
{60, 5481}, {61, 5580}, {62, 5679}, {63, 5778}, {64, 5877}, {65, 5976}, {66, 5985}, {67, 6084}, {68, 6183}, {69, 6282}, {70, 6381}, {71, 6480}, {72, 6579}, {73, 6678}, {74, 6777}, {75, 6876}, {76, 6975}, {77, 6984}, {78, 7083},
{79, 7182}, {80, 7281}, {81, 7380}, {82, 7479}, {83, 7578}, {84, 7677}, {85, 7776}, {86, 7875}, {87, 7974}, {88, 7983}, {89, 8082}, {90, 8181}, {91, 8280}, {92, 8379}, {93, 8478}, {94, 8577}, {95, 8676}, {96, 8775}, {97, 8874},
{98, 8973}, {99, 8982}, {100, 9081}, {101, 9180}, {102, 9279}, {103, 9378}, {104, 9477}, {105, 9576}, {106, 9675}, {107, 9774}, {108, 9873}, {109, 9972}, {110, 9981}, {111, 9990}, {112, 10089}, {113, 10188}, {114, 10287},
{115, 10386}, {116, 10485}, {117, 10584}, {118, 10683}, {119, 10782}, {120, 10881}, {121, 10980}, {122, 10989}, {123, 11088}, {124, 11187}, {125, 11286}, {126, 11385}, {127, 11484}, {128, 11583}, {129, 11682}, {130, 11781},
{131, 11880}, {132, 11979}, {133, 11988}, {134, 12087}, {135, 12186}, {136, 12285}, {137, 12384}, {138, 12483}, {139, 12582}, {140, 12681}, {141, 12780}, {142, 12879}, {143, 12978}, {144, 12987}, {145, 13086}, {146, 13185},
{147, 13284}, {148, 13383}, {149, 13482}, {150, 13581}, {151, 13680}, {152, 13779}, {153, 13878}, {154, 13977}, {155, 13986}, {156, 14085}, {157, 14184}, {158, 14283}, {159, 14382}, {160, 14481}, {161, 14580}, {162, 14679},
{163, 14778}, {164, 14877}, {165, 14976}, {166, 14985}, {167, 15084}, {168, 15183}, {169, 15282}, {170, 15381}, {171, 15480}, {172, 15579}, {173, 15678}, {174, 15777}, {175, 15876}, {176, 15975}, {177, 15984}, {178, 16083},
{179, 16182}, {180, 16281}, {181, 16380}, {182, 16479}, {183, 16578}, {184, 16677}, {185, 16776}, {186, 16875}, {187, 16974}, {188, 16983}, {189, 17082}, {190, 17181}, {191, 17280}, {192, 17379}, {193, 17478}, {194, 17577},
{195, 17676}, {196, 17775}, {197, 17874}, {198, 17973}, {199, 17982}, {200, 18081}, {201, 18180}, {202, 18279}, {203, 18378}, {204, 18477}, {205, 18576}, {206, 18675}, {207, 18774}, {208, 18873}, {209, 18972}, {210, 18981},
{211, 19080}, {212, 19179}, {213, 19278}, {214, 19377}, {215, 19476}, {216, 19575}, {217, 19674}, {218, 19773}, {219, 19872}, {220, 19971}, {221, 19980}, {222, 19989}, {223, 20088}, {224, 20187}, {225, 20286}, {226, 20385},
{227, 20484}, {228, 20583}, {229, 20682}, {230, 20781}, {231, 20880}, {232, 20979}, {233, 20988}, {234, 21087}, {235, 21186}, {236, 21285}, {237, 21384}, {238, 21483}, {239, 21582}, {240, 21681}, {241, 21780}, {242, 21879},
{243, 21978}, {244, 21987}, {245, 22086}, {246, 22185}, {247, 22284}, {248, 22383}, {249, 22482}, {250, 22581}, {251, 22680}, {252, 22779}, {253, 22878}, {254, 22977}, {255, 22986}, {256, 23085}, {257, 23184}, {258, 23283},
{259, 23382}, {260, 23481}, {261, 23580}, {262, 23679}, {263, 23778}, {264, 23877}, {265, 23976}, {266, 23985}, {267, 24084}, {268, 24183}, {269, 24282}, {270, 24381}, {271, 24480}, {272, 24579}, {273, 24678}, {274, 24777},
{275, 24876}, {276, 24975}, {277, 24984}, {278, 25083}, {279, 25182}, {280, 25281}, {281, 25380}, {282, 25479}, {283, 25578}, {284, 25677}, {285, 25776}, {286, 25875}, {287, 25974}, {288, 25983}, {289, 26082}, {290, 26181},
{291, 26280}, {292, 26379}, {293, 26478}, {294, 26577}, {295, 26676}, {296, 26775}, {297, 26874}, {298, 26973}, {299, 26982}, {300, 27081}, {301, 27180}, {302, 27279}, {303, 27378}, {304, 27477}, {305, 27576}, {306, 27675},
{307, 27774}, {308, 27873}, {309, 27972}, {310, 27981}, {311, 28080}, {312, 28179}, {313, 28278}, {314, 28377}, {315, 28476}, {316, 28575}, {317, 28674}, {318, 28773}, {319, 28872}, {320, 28971}, {321, 28980}, {322, 29079},
{323, 29178}, {324, 29277}, {325, 29376}, {326, 29475}, {327, 29574}, {328, 29673}, {329, 29772}, {330, 29871}, {331, 29970}, {332, 29979}, {333, 29988}, {334, 30087}, {335, 30186}, {336, 30285}, {337, 30384}, {338, 30483},
{339, 30582}, {340, 30681}, {341, 30780}, {342, 30879}, {343, 30978}, {344, 30987}, {345, 31086}, {346, 31185}, {347, 31284}, {348, 31383}, {349, 31482}, {350, 31581}, {351, 31680}, {352, 31779}, {353, 31878}, {354, 31977},
{355, 31986}, {356, 32085}, {357, 32184}, {358, 32283}, {359, 32382}, {360, 32481}, {361, 32580}, {362, 32679}, {363, 32778}, {364, 32877}, {365, 32976}, {366, 32985}, {367, 33084}, {368, 33183}, {369, 33282}, {370, 33381},
{371, 33480}, {372, 33579}, {373, 33678}, {374, 33777}, {375, 33876}, {376, 33975}, {377, 33984}, {378, 34083}, {379, 34182}, {380, 34281}, {381, 34380}, {382, 34479}, {383, 34578}, {384, 34677}, {385, 34776}, {386, 34875},
{387, 34974}, {388, 34983}, {389, 35082}, {390, 35181}, {391, 35280}, {392, 35379}, {393, 35478}, {394, 35577}, {395, 35676}, {396, 35775}, {397, 35874}, {398, 35973}, {399, 35982}, {400, 36081}, {401, 36180}, {402, 36279},
{403, 36378}, {404, 36477}, {405, 36576}, {406, 36675}, {407, 36774}, {408, 36873}, {409, 36972}, {410, 36981}, {411, 37080}, {412, 37179}, {413, 37278}, {414, 37377}, {415, 37476}, {416, 37575}, {417, 37674}, {418, 37773},
{419, 37872}, {420, 37971}, {421, 37980}, {422, 38079}, {423, 38178}, {424, 38277}, {425, 38376}, {426, 38475}, {427, 38574}, {428, 38673}, {429, 38772}, {430, 38871}, {431, 38970}, {432, 38979}, {433, 39078}, {434, 39177},
{435, 39276}, {436, 39375}, {437, 39474}, {438, 39573}, {439, 39672}, {440, 39771}, {441, 39870}, {442, 39969}, {443, 39978}, {444, 39987}, {445, 40086}, {446, 40185}, {447, 40284}, {448, 40383}, {449, 40482}, {450, 40581},
{451, 40680}, {452, 40779}, {453, 40878}, {454, 40977}, {455, 40986}, {456, 41085}, {457, 41184}, {458, 41283}, {459, 41382}, {460, 41481}, {461, 41580}, {462, 41679}, {463, 41778}, {464, 41877}, {465, 41976}, {466, 41985},
{467, 42084}, {468, 42183}, {469, 42282}, {470, 42381}, {471, 42480}, {472, 42579}, {473, 42678}, {474, 42777}, {475, 42876}, {476, 42975}, {477, 42984}, {478, 43083}, {479, 43182}, {480, 43281}, {481, 43380}, {482, 43479},
{483, 43578}, {484, 43677}, {485, 43776}, {486, 43875}, {487, 43974}, {488, 43983}, {489, 44082}, {490, 44181}, {491, 44280}, {492, 44379}, {493, 44478}, {494, 44577}, {495, 44676}, {496, 44775}, {497, 44874}, {498, 44973},
{499, 44982}, {500, 45081}, {501, 45180}, {502, 45279}, {503, 45378}, {504, 45477}, {505, 45576}, {506, 45675}, {507, 45774}, {508, 45873}, {509, 45972}, {510, 45981}, {511, 46080}, {512, 46179}, {513, 46278}, {514, 46377},
{515, 46476}, {516, 46575}, {517, 46674}, {518, 46773}, {519, 46872}, {520, 46971}, {521, 46980}, {522, 47079}, {523, 47178}, {524, 47277}, {525, 47376}, {526, 47475}, {527, 47574}, {528, 47673}, {529, 47772}, {530, 47871},
{531, 47970}, {532, 47979}, {533, 48078}, {534, 48177}, {535, 48276}, {536, 48375}, {537, 48474}, {538, 48573}, {539, 48672}, {540, 48771}, {541, 48870}, {542, 48969}, {543, 48978}, {544, 49077}, {545, 49176}, {546, 49275},
{547, 49374}, {548, 49473}, {549, 49572}, {550, 49671}, {551, 49770}, {552, 49869}, {553, 49968}, {554, 49977}, {555, 49986}, {556, 50085}, {557, 50184}, {558, 50283}, {559, 50382}, {560, 50481}, {561, 50580}, {562, 50679},
{563, 50778}, {564, 50877}, {565, 50976}, {566, 50985}, {567, 51084}, {568, 51183}, {569, 51282}, {570, 51381}, {571, 51480}, {572, 51579}, {573, 51678}, {574, 51777}, {575, 51876}, {576, 51975}, {577, 51984}, {578, 52083},
{579, 52182}, {580, 52281}, {581, 52380}, {582, 52479}, {583, 52578}, {584, 52677}, {585, 52776}, {586, 52875}, {587, 52974}, {588, 52983}, {589, 53082}, {590, 53181}, {591, 53280}, {592, 53379}, {593, 53478}, {594, 53577},
{595, 53676}, {596, 53775}, {597, 53874}, {598, 53973}, {599, 53982}, {600, 54081}, {601, 54180}, {602, 54279}, {603, 54378}, {604, 54477}, {605, 54576}, {606, 54675}, {607, 54774}, {608, 54873}, {609, 54972}, {610, 54981},
{611, 55080}, {612, 55179}, {613, 55278}, {614, 55377}, {615, 55476}, {616, 55575}, {617, 55674}, {618, 55773}, {619, 55872}, {620, 55971}, {621, 55980}, {622, 56079}, {623, 56178}, {624, 56277}, {625, 56376}, {626, 56475},
{627, 56574}, {628, 56673}, {629, 56772}, {630, 56871}, {631, 56970}, {632, 56979}, {633, 57078}, {634, 57177}, {635, 57276}, {636, 57375}, {637, 57474}, {638, 57573}, {639, 57672}, {640, 57771}, {641, 57870}, {642, 57969},
{643, 57978}, {644, 58077}, {645, 58176}, {646, 58275}, {647, 58374}, {648, 58473}, {649, 58572}, {650, 58671}, {651, 58770}, {652, 58869}, {653, 58968}, {654, 58977}, {655, 59076}, {656, 59175}, {657, 59274}, {658, 59373},
{659, 59472}, {660, 59571}, {661, 59670}, {662, 59769}, {663, 59868}, {664, 59967}, {665, 59976}, {666, 59985}, {667, 60084}, {668, 60183}, {669, 60282}, {670, 60381}, {671, 60480}, {672, 60579}, {673, 60678}, {674, 60777},
{675, 60876}, {676, 60975}, {677, 60984}, {678, 61083}, {679, 61182}, {680, 61281}, {681, 61380}, {682, 61479}, {683, 61578}, {684, 61677}, {685, 61776}, {686, 61875}, {687, 61974}, {688, 61983}, {689, 62082}, {690, 62181},
{691, 62280}, {692, 62379}, {693, 62478}, {694, 62577}, {695, 62676}, {696, 62775}, {697, 62874}, {698, 62973}, {699, 62982}, {700, 63081}, {701, 63180}, {702, 63279}, {703, 63378}, {704, 63477}, {705, 63576}, {706, 63675},
{707, 63774}, {708, 63873}, {709, 63972}, {710, 63981}, {711, 64080}, {712, 64179}, {713, 64278}, {714, 64377}, {715, 64476}, {716, 64575}, {717, 64674}, {718, 64773}, {719, 64872}, {720, 64971}, {721, 64980}, {722, 65079},
{723, 65178}, {724, 65277}, {725, 65376}, {726, 65475}, {727, 65574}, {728, 65673}, {729, 65772}, {730, 65871}, {731, 65970}, {732, 65979}, {733, 66078}, {734, 66177}, {735, 66276}, {736, 66375}, {737, 66474}, {738, 66573},
{739, 66672}, {740, 66771}, {741, 66870}, {742, 66969}, {743, 66978}, {744, 67077}, {745, 67176}, {746, 67275}, {747, 67374}, {748, 67473}, {749, 67572}, {750, 67671}, {751, 67770}, {752, 67869}, {753, 67968}, {754, 67977},
{755, 68076}, {756, 68175}, {757, 68274}, {758, 68373}, {759, 68472}, {760, 68571}, {761, 68670}, {762, 68769}, {763, 68868}, {764, 68967}, {765, 68976}, {766, 69075}, {767, 69174}, {768, 69273}, {769, 69372}, {770, 69471},
{771, 69570}, {772, 69669}, {773, 69768}, {774, 69867}, {775, 69966}, {776, 69975}, {777, 69984}, {778, 70083}, {779, 70182}, {780, 70281}, {781, 70380}, {782, 70479}, {783, 70578}, {784, 70677}, {785, 70776}, {786, 70875},
{787, 70974}, {788, 70983}, {789, 71082}, {790, 71181}, {791, 71280}, {792, 71379}, {793, 71478}, {794, 71577}, {795, 71676}, {796, 71775}, {797, 71874}, {798, 71973}, {799, 71982}, {800, 72081}, {801, 72180}, {802, 72279},
{803, 72378}, {804, 72477}, {805, 72576}, {806, 72675}, {807, 72774}, {808, 72873}, {809, 72972}, {810, 72981}, {811, 73080}, {812, 73179}, {813, 73278}, {814, 73377}, {815, 73476}, {816, 73575}, {817, 73674}, {818, 73773},
{819, 73872}, {820, 73971}, {821, 73980}, {822, 74079}, {823, 74178}, {824, 74277}, {825, 74376}, {826, 74475}, {827, 74574}, {828, 74673}, {829, 74772}, {830, 74871}, {831, 74970}, {832, 74979}, {833, 75078}, {834, 75177},
{835, 75276}, {836, 75375}, {837, 75474}, {838, 75573}, {839, 75672}, {840, 75771}, {841, 75870}, {842, 75969}, {843, 75978}, {844, 76077}, {845, 76176}, {846, 76275}, {847, 76374}, {848, 76473}, {849, 76572}, {850, 76671},
{851, 76770}, {852, 76869}, {853, 76968}, {854, 76977}, {855, 77076}, {856, 77175}, {857, 77274}, {858, 77373}, {859, 77472}, {860, 77571}, {861, 77670}, {862, 77769}, {863, 77868}, {864, 77967}, {865, 77976}, {866, 78075},
{867, 78174}, {868, 78273}, {869, 78372}, {870, 78471}, {871, 78570}, {872, 78669}, {873, 78768}, {874, 78867}, {875, 78966}, {876, 78975}, {877, 79074}, {878, 79173}, {879, 79272}, {880, 79371}, {881, 79470}, {882, 79569},
{883, 79668}, {884, 79767}, {885, 79866}, {886, 79965}, {887, 79974}, {888, 79983}, {889, 80082}, {890, 80181}, {891, 80280}, {892, 80379}, {893, 80478}, {894, 80577}, {895, 80676}, {896, 80775}, {897, 80874}, {898, 80973},
{899, 80982}, {900, 81081}, {901, 81180}, {902, 81279}, {903, 81378}, {904, 81477}, {905, 81576}, {906, 81675}, {907, 81774}, {908, 81873}, {909, 81972}, {910, 81981}, {911, 82080}, {912, 82179}, {913, 82278}, {914, 82377},
{915, 82476}, {916, 82575}, {917, 82674}, {918, 82773}, {919, 82872}, {920, 82971}, {921, 82980}, {922, 83079}, {923, 83178}, {924, 83277}, {925, 83376}, {926, 83475}, {927, 83574}, {928, 83673}, {929, 83772}, {930, 83871},
{931, 83970}, {932, 83979}, {933, 84078}, {934, 84177}, {935, 84276}, {936, 84375}, {937, 84474}, {938, 84573}, {939, 84672}, {940, 84771}, {941, 84870}, {942, 84969}, {943, 84978}, {944, 85077}, {945, 85176}, {946, 85275},
{947, 85374}, {948, 85473}, {949, 85572}, {950, 85671}, {951, 85770}, {952, 85869}, {953, 85968}, {954, 85977}, {955, 86076}, {956, 86175}, {957, 86274}, {958, 86373}, {959, 86472}, {960, 86571}, {961, 86670}, {962, 86769},
{963, 86868}, {964, 86967}, {965, 86976}, {966, 87075}, {967, 87174}, {968, 87273}, {969, 87372}, {970, 87471}, {971, 87570}, {972, 87669}, {973, 87768}, {974, 87867}, {975, 87966}, {976, 87975}, {977, 88074}, {978, 88173},
{979, 88272}, {980, 88371}, {981, 88470}, {982, 88569}, {983, 88668}, {984, 88767}, {985, 88866}, {986, 88965}, {987, 88974}, {988, 89073}, {989, 89172}, {990, 89271}, {991, 89370}, {992, 89469}, {993, 89568}, {994, 89667},
{995, 89766}, {996, 89865}, {997, 89964}, {998, 89973}, {999, 89982}, {1000, 90081}, {1001, 90180}, {1002, 90279}, {1003, 90378}, {1004, 90477}, {1005, 90576}, {1006, 90675}, {1007, 90774}, {1008, 90873}, {1009, 90972},
{1010, 90981}, {1011, 91080}, {1012, 91179}, {1013, 91278}, {1014, 91377}, {1015, 91476}, {1016, 91575}, {1017, 91674}, {1018, 91773}, {1019, 91872}, {1020, 91971}, {1021, 91980}, {1022, 92079}, {1023, 92178}, {1024, 92277},
{1025, 92376}, {1026, 92475}, {1027, 92574}, {1028, 92673}, {1029, 92772}, {1030, 92871}, {1031, 92970}, {1032, 92979}, {1033, 93078}, {1034, 93177}, {1035, 93276}, {1036, 93375}, {1037, 93474}, {1038, 93573}, {1039, 93672},
{1040, 93771}, {1041, 93870}, {1042, 93969}, {1043, 93978}, {1044, 94077}, {1045, 94176}, {1046, 94275}, {1047, 94374}, {1048, 94473}, {1049, 94572}, {1050, 94671}, {1051, 94770}, {1052, 94869}, {1053, 94968}, {1054, 94977},
{1055, 95076}, {1056, 95175}, {1057, 95274}, {1058, 95373}, {1059, 95472}, {1060, 95571}, {1061, 95670}, {1062, 95769}, {1063, 95868}, {1064, 95967}, {1065, 95976}, {1066, 96075}, {1067, 96174}, {1068, 96273}, {1069, 96372},
{1070, 96471}, {1071, 96570}, {1072, 96669}, {1073, 96768}, {1074, 96867}, {1075, 96966}, {1076, 96975}, {1077, 97074}, {1078, 97173}, {1079, 97272}, {1080, 97371}, {1081, 97470}, {1082, 97569}, {1083, 97668}, {1084, 97767},
{1085, 97866}, {1086, 97965}, {1087, 97974}, {1088, 98073}, {1089, 98172}, {1090, 98271}, {1091, 98370}, {1092, 98469}, {1093, 98568}, {1094, 98667}, {1095, 98766}, {1096, 98865}, {1097, 98964}, {1098, 98973}, {1099, 99072},
{1100, 99171}, {1101, 99270}, {1102, 99369}, {1103, 99468}, {1104, 99567}, {1105, 99666}, {1106, 99765}, {1107, 99864}, {1108, 99963}, {1109, 99972}, {1110, 99981}, {1111, 99990}, {1112, 100089}, {1113, 100188}, {1114, 100287},
{1115, 100386}, {1116, 100485}, {1117, 100584}, {1118, 100683}, {1119, 100782}, {1120, 100881}, {1121, 100980}, {1122, 100989}, {1123, 101088}, {1124, 101187}, {1125, 101286}, {1126, 101385}, {1127, 101484}, {1128, 101583},
{1129, 101682}, {1130, 101781}, {1131, 101880}, {1132, 101979}, {1133, 101988}, {1134, 102087}, {1135, 102186}, {1136, 102285}, {1137, 102384}, {1138, 102483}, {1139, 102582}, {1140, 102681}, {1141, 102780}, {1142, 102879},
{1143, 102978}, {1144, 102987}, {1145, 103086}, {1146, 103185}, {1147, 103284}, {1148, 103383}, {1149, 103482}, {1150, 103581}, {1151, 103680}, {1152, 103779}, {1153, 103878}, {1154, 103977}, {1155, 103986}, {1156, 104085},
{1157, 104184}, {1158, 104283}, {1159, 104382}, {1160, 104481}, {1161, 104580}, {1162, 104679}, {1163, 104778}, {1164, 104877}, {1165, 104976}, {1166, 104985}, {1167, 105084}, {1168, 105183}, {1169, 105282}, {1170, 105381},
{1171, 105480}, {1172, 105579}, {1173, 105678}, {1174, 105777}, {1175, 105876}, {1176, 105975}, {1177, 105984}, {1178, 106083}, {1179, 106182}, {1180, 106281}, {1181, 106380}, {1182, 106479}, {1183, 106578}, {1184, 106677},
{1185, 106776}, {1186, 106875}, {1187, 106974}, {1188, 106983}, {1189, 107082}, {1190, 107181}, {1191, 107280}, {1192, 107379}, {1193, 107478}, {1194, 107577}, {1195, 107676}, {1196, 107775}, {1197, 107874}, {1198, 107973},
{1199, 107982}, {1200, 108081}, {1201, 108180}, {1202, 108279}, {1203, 108378}, {1204, 108477}, {1205, 108576}, {1206, 108675}, {1207, 108774}, {1208, 108873}, {1209, 108972}, {1210, 108981}, {1211, 109080}, {1212, 109179},


太小气了！不让发！


{9907, 891864}, {9908, 891963}, {9909, 891972}, {9910, 892071}, {9911, 892170}, {9912, 892269}, {9913, 892368}, {9914, 892467}, {9915, 892566}, {9916, 892665}, {9917, 892764}, {9918, 892863}, {9919, 892962}, {9920, 892971},
{9921, 893070}, {9922, 893169}, {9923, 893268}, {9924, 893367}, {9925, 893466}, {9926, 893565}, {9927, 893664}, {9928, 893763}, {9929, 893862}, {9930, 893961}, {9931, 893970}, {9932, 894069}, {9933, 894168}, {9934, 894267},
{9935, 894366}, {9936, 894465}, {9937, 894564}, {9938, 894663}, {9939, 894762}, {9940, 894861}, {9941, 894960}, {9942, 894969}, {9943, 895068}, {9944, 895167}, {9945, 895266}, {9946, 895365}, {9947, 895464}, {9948, 895563},
{9949, 895662}, {9950, 895761}, {9951, 895860}, {9952, 895959}, {9953, 895968}, {9954, 896067}, {9955, 896166}, {9956, 896265}, {9957, 896364}, {9958, 896463}, {9959, 896562}, {9960, 896661}, {9961, 896760}, {9962, 896859},
{9963, 896958}, {9964, 896967}, {9965, 897066}, {9966, 897165}, {9967, 897264}, {9968, 897363}, {9969, 897462}, {9970, 897561}, {9971, 897660}, {9972, 897759}, {9973, 897858}, {9974, 897957}, {9975, 897966}, {9976, 898065},
{9977, 898164}, {9978, 898263}, {9979, 898362}, {9980, 898461}, {9981, 898560}, {9982, 898659}, {9983, 898758}, {9984, 898857}, {9985, 898956}, {9986, 898965}, {9987, 899064}, {9988, 899163}, {9989, 899262}, {9990, 899361},
{9991, 899460}, {9992, 899559}, {9993, 899658}, {9994, 899757}, {9995, 899856}, {9996, 899955}, {9997, 899964}, {9998, 899973}, {9999, 899982}, {10000, 900081}}

Transpose[{Range@Length@#, #}] &[Join @@ Table[100 n - Tr@IntegerDigits[n] - 9 Range[IntegerExponent[10 n, 10], 1, -1], {n, 9001}]]