1000以内的质数个数计算方法：

朱明君 · 发表于 2020-12-9 09:39

本帖最后由朱明君于 2022-4-20 12:15 编辑

1000以内的质数个数计算方法：

1000/2-（166+66+37+20+16+10+8+6+2+1）=168个质数，

第1步， 1000/2=500个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步， (500-2)/3=166，
第3步， (500-8)/5=98，{98+[(5-1)/2]-2}/3=32， 98-32=66，
第4步， (500-18)/7=68, {68+[(7-1)/2]-2}/3=23，
                                    {68+[(7-1)/2]-8}/5=12， {12+(5-1)/2-2}/3= 4，12-4=8，
                                       68-23-8=37，
第5步， (500-50)/11=40, {40+[(11-1)/2]-2}/3=14， {[(11+1)/2]-2}/3=1，14-1=13,
                                          {40+[(11-1)/2]-8}/5=7， {7+[(5-1)/2]-2}/3= 2， 7-2=5,
                                          {40+[(11-1)/2]-18}/7=3， {3+[(7-1)/2]-2}/3= 1， 3-1=2,
                                          40-13-5-2=20,
第6步， (500-72)/13=32， {32+[(13-1)/2]-2}/3=12， {[(13+1)/2]-2}/3=1，12-1=11,
                                          {32+[(13-1)/2]-8}/5=6， {6+[(5-1)/2]-2}/3= 2， 6-2=4,
                                          {32+[(13-1)/2]-18}/7=2， {2+[(7-1)/2]-2}/3= 1， 2-1=1,
                                          32-11-4-1=16,
第7步，(500-128)/17=21,  {21+[(17-1)/2]-2}/3=9， {[(17+1)/2]-2}/3=2，9-2=7,
                                          {21+[(17-1)/2]-8}/5=4， {4+[(5-1)/2]-2}/3= 1， 4-1=3,
                                          {21+[(17-1)/2]-18}/7=1，
′
                                          21-7-3-1=10,
第8步，(500-162/)19=17, {17+[(19-1)/2]-2}/3=8，  {[(19+1)/2]-2}/3=2，8-2=6,
                                          {17+[(19-1)/2]-8}/5=3， {3+[(5-1)/2]-2}/3= 1，3-1=2,
                                          {17+[(19-1)/2]-18}/7=1，
                                          17-6-2-1=8,
第9步，(500-242)/23=11,  {11+[(23-1)/2]-2}/3=6，  {[(23+1)/2]-2}/3=3，6-3=3,
                                          {11+[(23-1)/2]-8}/5=2，
                                          11-3-2=6,
第10步, (500-392)/29=3，{3+[(29-1)/2]-2}/3=5，  {[(29+1)/2]-2}/3=4，5-4=1,
                                       {3+ [(29-1)/2]-8}/5=1，  {[(29+1)/2]-8}/5=1，1-1=0,
                                          3-1-0=2,
第11步, (500-450)/31=1，
      500-166-66-37-20-16-10-8-6-2-1=168。

朱明君 · 发表于 2020-12-9 18:17

本帖最后由朱明君于 2022-4-25 13:48 编辑

实例500以内的质数的个数
第1步， 500/2=250个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步， (250-2)/3=82，
第3步， (250-8)/5=48，{48+[(5-1)/2]-2}/3=16，48-16=32，
第4步， (250-18)/7=33, {33+[(7-1)/2]-2}/3=11，
                                    {33+[(7-1)/2]-8}/5=5， {5+[(5-1)/2]-2}/3=1， 5-1=4 ,
                                    33-11-4=18，
第5步，(250-50)/11=18，{18+[(11-1)/2]-2}/3=7，[(11+1)/2-2]/3=1, 7-1=6,
                                       {18+[(11-1)/2]-8}/5=3，{3+[(5-1)/2]-2}/3=1， 3-1=2,
                                       18-6-2=10，
第6步, (250-72)/13=13, {13+[(13-1)/2]-2}/3=5，[(13+1)/2-2]/3=1, 5-1=4,
                                       {13+[(13-1)/2]-8}/5=2，
                                       13-4-2=7，
第7步，(250-128)/17=7, {7+[(17-1)/2]-2}/3=4，[(17+1)/2-2]/3=2, 4-2=2,
                                       {7+[(17-1)/2]-8}/5=1，
                                          7-2-1=4，
第8步，(250-162)/19=4，{4+[(19-1)/2]-2}/3=3，[(19+1)/2-2]/3=2, 3-2=1,
                                       {4+[(19-1)/2]-8}/5=1，
                                          4-1-1=2，

500/2-(82+32+18+10+7+4+2)=95个质数，

朱明君 · 发表于 2020-12-9 19:05

本帖最后由朱明君于 2020-12-10 23:55 编辑

300以内的质数个数计算方法，

300/2-(49+19+10+5+4+1)=62个质数，

第1步，300/2=150个奇数，为了计算简捷，我们直接将奇数1改成质数2，
第2步，(150-2)/3=49，
第3步，(150-8)/5=28，  {28+[(5-1)/2]-2}/3=9, 28-9=19,
第4步，(150-18)/7=18，{18+[(7-1)/2]-2}/3=6,
                                       {18+[(7-1)/2]-8}/5=2,
                                       18-6-2=10,
第5步，(150-50)/11=9, {9+[(11-1)/2]-2}/3=4, [(11+1)/2-2]/3=1, 4-1=3，
                                       {9+[(11-1)/2]-8}/5=1,
                                       9-3-1=5,
第6步  (150-72)/13=6, {6+[(13-1)/2]-2}/3=3, [(13+1)/2-2]/3=1, 3-1=2，
                                       6-2=4,
第7步，(150-128)/17=1,

朱明君 · 发表于 2020-12-9 19:21

本帖最后由朱明君于 2020-12-9 11:25 编辑

168以内的质数个数计算方法：

168/2-(27+10+6+2)=39个质数，

第1步，168/2=84个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步，(84-2)/3=27，
第3步，(84-8)/5=15，{15+[(5-1)/2]-2}/3=5,    15-5=10，
第4步，(84-18)/7=9，{9+[(7-1)/2]-2}/3=3,    9-3=6，
第5步，(84-50)/11=3, {3+[(11-1)/2]-2}/3=2, [(11+1)/2-2]/3=1,  2-1=1,
                                 3-1=2，

朱明君 · 发表于 2020-12-9 19:40

本帖最后由朱明君于 2020-12-9 11:43 编辑

100以内的质数个数计算方法：

100/2-(16+6+3)=25个质数，

第1步，100/2=50个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步，(50-2)/3=16，
第3步，(50-8)/5=8，  {8+[(5-1)/2]-2}/3=2,    8-2=6，
第4步，(50-18)/7=4，{4+[(7-1)/2]-2}/3=1,    4-1=3，
,

朱明君 · 发表于 2020-12-16 20:55

本帖最后由朱明君于 2021-1-2 14:12 编辑

奇质数的对应数计算公式：设奇质数为X,对应数为y则{(X^2+1)/2}-X=y,
3=2, 5=8, 7=18, 11=50, 13=72， 17=128，  19=162，-------。

10000以内的质数个数计算方法：

10000/2-（+）=1229个质数，

第1步， 10000/2=5000个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步， (5000-2)/3=1666，
第3步， (5000-8)/5=998，{998+[(5-1)/2]/3=332， 998-332=666，
第4步， (5000-18)/7=711,    [1], {711+[(7-1)/2]-2}/3=237,
                                                [2], {711+[(7-1)/2]-8}/5=141, {141+[(5-1)/2]-2}/3=47, 141-47=94,
                                 711-237-94=380,
第5步， (5000-50)/11=450,    [1], {450+[(11-1)/2]-2}/3=151, {[(11+1)/2]-2}/3=1, 151-1=150,
                                                [2], {450+[(11-1)/2]-8}/5=89,    {89+[(5-1)/2]-2}/3=29, 89-29=60,
                                                [3], {450+[(11-1)/2]-18}/7=62, {62+[(7-1)/2]-2}/3=21,
                                                                                                      {62+[(7-1)/2]-8}/5=11, [11+(5-1)-2)/3=3, 11-3=8,
                                                                                             62-21-8=33,
                                    450-150-60-33=207,
第6步， (5000-72)/13=379,    [1], {379+[(13-1)/2]-2}/3=127,    {[(13+1)/2]-2}/3=1, 127-1=126,
                                                [2], {379+[(13-1)/2]-8}/5=75,    {75+[(5-1)/2]-2}/3=25, 75-25=50,
                                                [3], {379+[(13-1)/2]-18}/7=52, {52+[(7-1)/2]-2}/3=17,
                                                                                                      {52+[(7-1)/2]-8}/5=9, [9+(5-1)-2)/3=3, 9-3=6,
                                                                                             52-17-9=26,
                                                [4], {379+[(13-1)/2]-50}/11=30,  {30+[(11-1)/2]-2}/3= 11，  [(11+1)/2-2]/3=1，11-1=10,
                                                                                                      {30+[(11-1)/2]-8}/5= 5  ，  [5+(5-1)-2)/3=1, 5-1=4,
                                                                                                      {30+[(11-1)/2]-18}/7= 2，  [2+(7-1)-2)/3=1, 2-1=1,
                                                                                                30-10-4-1=15,
                                    379-126-50-26-15=162,
第7步， (5000-128)/17=286, [1], {286+[(17-1)/2]-2}/3=97,    {[(17+1)/2]-2}/3=2, 97-2=95,
                                                [2], {286+[(17-1)/2]-8}/5=57,    {57+[(5-1)/2]-2}/3=19, 57-19=38,
                                                [3], {286+[(17-1)/2]-18}/7=39, {39+[(7-1)/2]-2}/3=13,
                                                                                                      {39+[(7-1)/2]-8}/5=6,    [6+(5-1)-2)/3=2, 6-2=4,
                                                                                             39-13-4=22,
                                                [4], {286+[(17-1)/2]-50}/11=22,  {22+[(11-1)/2]-2}/3=8, [(11+1)/2-2]/3=1，8-1=7,
                                                                                                      {22+[(11-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                                      {22+[(11-1)/2]-18}/7=1,
                                                                                                22-7-2-1=12,
                                                [5], {286+[(17-1)/2]-72}/13=17,  {17+[(13-1)/2]-2}/3=7, [(13+1)/2-2]/3=1，7-1=6,
                                                                                                      {17+[(13-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                             17-6-2=9,
                                 286-95-38-22-12-9=110,
第8步， (5000-162)/19=254, [1], {254+[(19-1)/2]-2}/3=87,    {[(19+1)/2]-2}/3=2, 87-2=85,
                                                [2], {254+[(19-1)/2]-8}/5=51,    {51+[(5-1)/2]-2}/3=17, 51-17=34,
                                                [3], {254+[(19-1)/2]-18}/7=35, {35+[(7-1)/2]-2}/3=12,
                                                                                                      {35+[(7-1)/2]-8}/5=6,    [6+(5-1)-2)/3=2, 6-2=4,
                                                                                             35-12-4=19,
                                                [4], {254+[(19-1)/2]-50}/11=19,  {19+[(11-1)/2]-2}/3=7, [(11+1)/2-2]/3=1，7-1=6,
                                                                                                      {19+[(11-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                             19-6-2-1=11,
                                                [5], {254+[(19-1)/2]-72}/13=14,  {14+[(13-1)/2]-2}/3=6, [(13+1)/2-2]/3=1，6-1=5,
                                                                                                      {14+[(13-1)/2]-8}/5=2,
                                                                                             14-5-2=7,
                                                [6], {254+[(19-1)/2]-128}/17=7,  {7+[(17-1)/2]-2}/3=4, [(17+1)/2-2]/3=2，4-2=2,
                                                                                                      {7+[(17-1)/2]-8}/5=1
,                                                                                                 7-2-1=4,
                                       254-85-34-19-11-7-4=94,
第9步， (5000-242)/23=206, [1], {206+[(23-1)/2]-2}/3=71,    {[(23+1)/2]-2}/3=3, 71-3=68,
                                                [2], {206+[(23-1)/2]-8}/5=41,    {41+[(5-1)/2]-2}/3=13, 41-13=28,
                                                [3], {206+[(23-1)/2]-18}/7=28, {28+[(7-1)/2]-2}/3=9,
                                                                                                      {28+[(7-1)/2]-8}/5=4,    [4+(5-1)-2)/3=1, 4-1=3,
                                                                                          28-9-3=16,
                                                [4], {206+[(23-1)/2]-50}/11=15,  {15+[(11-1)/2]-2}/3=6, [(11+1)/2-2]/3=1，6-1=5,
                                                                                                      {15+[(11-1)/2]-8}/5=2,
                                                                                             15-5-2=8,
                                                [5], {206+[(23-1)/2]-72}/13=11,  {11+[(13-1)/2]-2}/3=5, [(13+1)/2-2]/3=1，5-1=4,
                                                                                                      {11+[(13-1)/2]-8}/5=1,
                                                                                             11-4-1=6,
                                                [6], {206+[(23-1)/2]-128}/17=5,  {5+[(17-1)/2]-2}/3=3, [(17+1)/2-2]/3=2，3-2=1,
                                                                                                      {5+[(17-1)/2]-8}/5=1
,                                                                                                 5-1-1=3,
                                                [7], {206+[(23-1)/2]-162}/19=2,  {2+[(19-1)/2]-2}/3=3, [(19+1)/2-2]/3=2，3-2=1,
                                                                                                2-1=1,
                                       206-68-28-16-8-6-3-1=76,
第10步，(5000-392)/29=158,
                                                   [1], {158+[(29-1)/2]-2}/3=56,    {[(29+1)/2]-2}/3=4, 56-4=52,
                                                   [2], {158+[(29-1)/2]-8}/5=32,    {32+[(5-1)/2]-2}/3=10,  32-10=22,
                                                         {[(29+1)/2]-8}/5=1,
                                                         22-1=21,
                                                   [3], {158+[(29-1)/2]-18}/7=22, {22+[(7-1)/2]-2}/3=7,  22-7=15
                                                                                                      {22+[(7-1)/2]-8}/5=3,    {3+[(5-1)/2]-2}/3=1,  3-1=2,
                                                         15-2=13,
                                                   [4], {158+[(29-1)/2]-50}/11=11,  {11+[(11-1)/2]-2}/3=4, [(11+1)/2-2]/3=1,  4-1=3
                                                                                                      {11+[(11-1)/2]-8}/5=1,
                                                         11-(4-1)-1=7,
                                                   [5], {158+[(29-1)/2]-72}/13=7, {7+[(13-1)/2]-2}/3=3,    [(13+1)/2-2]/3=1,  3-1=2,
                                                                                                      {7+[(13-1)/2]-8}/5=1,
                                                         7-(3-1)-2=4，
                                                   [6], {158+[(29-1)/2]-128}/17=2,
               158-52-21-13-7-4-2=59,
第11步，(5000-450)/31=146,    [1], {146+[(31-1)/2]-2}/3=53,    {[(31+1)/2]-2}/3=4, 53-4=49,
                                                   [2], {146+[(31-1)/2]-8}/5=30,    {[(31+1)/2]-8}/5=1,
                                                         {30+[(5-1)/2]-2}/3=10,
                                                         30-1-10=19,
                                                   [3], {146+[(31-1)/2]-18}/7=20,    {20+[(7-1)/2]-2}/3=7,
                                                                                                         {20+[(7-1)/2]-8}/5=3,  {3+[(5-1)/2]-2}/3=1,  3-1=2,
                                                         20-7-2=11,
                                                [4], {146+[(31-1)/2]-50}/11=10, {10+[(11-1)/2]-2}/3=4, {[(11+1)/2]-2}/3=1, 4-1=3
                                                                                                         {10+[(11-1)/2]-8}/5=1,
                                                         10-3-1=6
                                                   [5], {146+[(31-1)/2]-72}/13=6,    {6+[(13-1)/2]-2}/3=3,
                                                                                                         {[(13+1)/2]-2}/3=1,
                                                         6-(3-1)=4
                                                   [6], {146+[(31-1)/2]-128}/17=1,
                                       146-49-19-11-6-4-1=56,

朱明君 · 发表于 2020-12-19 21:35

本帖最后由朱明君于 2021-1-3 12:47 编辑

10000以内的质数个数计算方法：

10000/2-（1666+666+380+206+162+110+94+76+59+51+46+42+38+33+27+24+21+17+15+12+9+8+6+3）=1229个质数，

第1步， 10000/2=5000个奇数，为了计算简捷，我们直接将奇数1改成质数2
第2步， (5000-2)/3=1666，
第3步， (5000-8)/5=998，{998+[(5-1)/2]/3=332， 998-332=666，
第4步， (5000-18)/7=711,    (711-1)×2+7=1427,
                                                [1], {[(1427+1)/2]-2}/3=237,
                                                [2], {[(1427+1)/2]-8}/5=141, {141+[(5-1)/2]-2}/3=47, 141-47=94,
                                             711-237-94=380,
第5步， (5000-50)/11=450,    (450-1)×2+11=909,
                                                [1], {[(909+1)/2]-2}/3=151, {[(11+1)/2]-2}/3=1, 151-1=150,
                                                [2], {[(909+1)/2]-8}/5=89,    {89+[(5-1)/2]-2}/3=29, 89-29=60,
                                                [3], {[(909+1)/2]-18}/7=62, {62+[(7-1)/2]-2}/3=20,
                                                                                                {62+[(7-1)/2]-8}/5=11, [11+(5-1)-2)/3=3, 11-3=8,
                                                                                             62-20-8=34,
                                    450-150-60-34=206,
第6步， (5000-72)/13=379,    (379-1)×2+13=769,
                                                [1], {[(769+1)/2]-2}/3=127, {[(13+1)/2]-2}/3=1, 127-1=126,
                                                [2], {[(769+1)/2]-8}/5=75,    {75+[(5-1)/2]-2}/3=25, 75-25=50,
                                                [3], {[(769+1)/2]-18}/7=52, {52+[(7-1)/2]-2}/3=17,
                                                                                                {52+[(7-1)/2]-8}/5=9, [9+(5-1)-2)/3=3, 9-3=6,
                                                                                             52-17-9=26,
                                                [4], {[(769+1)/2]-50}/11=30,  {30+[(11-1)/2]-2}/3= 11，  [(11+1)/2-2]/3=1，11-1=10,
                                                                                                {30+[(11-1)/2]-8}/5= 5  ，  [5+(5-1)-2)/3=1, 5-1=4,
                                                                                                {30+[(11-1)/2]-18}/7= 2，  [2+(7-1)-2)/3=1, 2-1=1,
                                                                                             30-10-4-1=15,
                                    379-126-50-26-15=162,
第7步， (5000-128)/17=286, (286-1)×2+17=587,
                                                [1], {[(587+1)/2]-2}/3=97,    {[(17+1)/2]-2}/3=2, 97-2=95,
                                                [2], {[(587+1)/2]-8}/5=57,    {57+[(5-1)/2]-2}/3=19, 57-19=38,
                                                [3], {[(587+1)/2]-18}/7=39, {39+[(7-1)/2]-2}/3=13,
                                                                                                {39+[(7-1)/2]-8}/5=6,    [6+(5-1)-2)/3=2, 6-2=4,
                                                                                             39-13-4=22,
                                                [4], {[(587+1)/2]-50}/11=22,  {22+[(11-1)/2]-2}/3=8, [(11+1)/2-2]/3=1，8-1=7,
                                                                                                {22+[(11-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                                {22+[(11-1)/2]-18}/7=1,
                                                                                             22-7-2-1=12,
                                                [5], {[(587+1)/2]-72}/13=17,  {17+[(13-1)/2]-2}/3=7, [(13+1)/2-2]/3=1，7-1=6,
                                                                                                {17+[(13-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                             17-6-2=9,
                                       286-95-38-22-12-9=110,

朱明君 · 发表于 2020-12-19 22:00

本帖最后由朱明君于 2021-1-2 14:38 编辑

第8步， (5000-162)/19=254, (254-1)×2+19=525,
                                                [1], {[(525+1)/2]-2}/3=87,    {[(19+1)/2]-2}/3=2, 87-2=85,
                                                [2], {[(525+1)/2]-8}/5=51,    {51+[(5-1)/2]-2}/3=17, 51-17=34,
                                                [3], {[(525+1)/2]-18}/7=35, {35+[(7-1)/2]-2}/3=12,
                                                                                                {35+[(7-1)/2]-8}/5=6,    [6+(5-1)-2)/3=2, 6-2=4,
                                                                                             35-12-4=19,
                                                [4], {[(525+1)/2]-50}/11=19,  {19+[(11-1)/2]-2}/3=7, [(11+1)/2-2]/3=1，7-1=6,
                                                                                                {19+[(11-1)/2]-8}/5=3, [3+(5-1)-2)/3=1, 3-1=2,
                                                                                             19-6-2-1=11,
                                                [5], {[(525+1)/2]-72}/13=14,  {14+[(13-1)/2]-2}/3=6, [(13+1)/2-2]/3=1，6-1=5,
                                                                                                {14+[(13-1)/2]-8}/5=2,
                                                                                             14-5-2=7,
                                                [6], {[(525+1)/2]-128}/17=7,  {7+[(17-1)/2]-2}/3=4, [(17+1)/2-2]/3=2，4-2=2,
                                                                                                {7+[(17-1)/2]-8}/5=1
,                                                                                              7-2-1=4,
                                       254-85-34-19-11-7-4=94,
第9步， (5000-242)/23=206, (206-1)×2+23=433,
                                                [1], {[(433+1)/2]-2}/3=71,    {[(23+1)/2]-2}/3=3, 71-3=68,
                                                [2], {[(433+1)/2]-8}/5=41,    {41+[(5-1)/2]-2}/3=13, 41-13=28,
                                                [3], {[(433+1)/2]-18}/7=28, {28+[(7-1)/2]-2}/3=9,
                                                                                                {28+[(7-1)/2]-8}/5=4,    [4+(5-1)-2)/3=1, 4-1=3,
                                                                                          28-9-3=16,
                                                [4], {[(433+1)/2]-50}/11=15,  {15+[(11-1)/2]-2}/3=6, [(11+1)/2-2]/3=1，6-1=5,
                                                                                                {15+[(11-1)/2]-8}/5=2,
                                                                                             15-5-2=8,
                                                [5], {[(433+1)/2]-72}/13=11,  {11+[(13-1)/2]-2}/3=5, [(13+1)/2-2]/3=1，5-1=4,
                                                                                                {11+[(13-1)/2]-8}/5=1,
                                                                                             11-4-1=6,
                                                [6], {[(433+1)/2]-128}/17=5,  {5+[(17-1)/2]-2}/3=3, [(17+1)/2-2]/3=2，3-2=1,
                                                                                                      {5+[(17-1)/2]-8}/5=1
,                                                                                              5-1-1=3,
                                                [7], {[(433+1)/2]-162}/19=2,  {2+[(19-1)/2]-2}/3=3, [(19+1)/2-2]/3=2，3-2=1,
                                                                                             2-1=1,
                                       206-68-28-16-8-6-3-1=76,
第10步，(5000-392)/29=158,    (158-1)×2+31=343,
                                                   [1], {[(343+1)/2]-2}/3=56,    {[(29+1)/2]-2}/3=4, 56-4=52,
                                                   [2], {[(343+1)/2]-8}/5=32,    {32+[(5-1)/2]-2}/3=10,  32-10=22,
                                                         {[(29+1)/2]-8}/5=1,
                                                         22-1=21,
                                                   [3], {[(343+1)/2]-18}/7=22,    {22+[(7-1)/2]-2}/3=7,  22-7=15
                                                                                                   {22+[(7-1)/2]-8}/5=3, {3+[(5-1)/2]-2}/3=1,  3-1=2,
                                                         15-2=13,
                                                   [4], {[(343+1)/2]-50}/11=11, {11+[(11-1)/2]-2}/3=4, [(11+1)/2-2]/3=1,  4-1=3
                                                                                                   {11+[(11-1)/2]-8}/5=1,
                                                         11-(4-1)-1=7,
                                                   [5], {[(343+1)/2]-72}/13=7,    {7+[(13-1)/2]-2}/3=3,    [(13+1)/2-2]/3=1,  3-1=2,
                                                                                                      {7+[(13-1)/2]-8}/5=1,
                                                         7-(3-1)-2=4，
                                                   [6], {[(343+1)/2]-128}/17=2,
                                          158-52-21-13-7-4-2=59,
第11步，(5000-450)/31=146,    (146-1)×2+31=321,
                                                   [1], {[(321+1)/2]-2}/3=53,    {[(31+1)/2]-2}/3=4, 53-4=49,
                                                   [2], {[(321+1)/2]-8}/5=30,    {30+[(5-1)/2]-2}/3=10,  30-10=20,
                                                         {[(31+1)/2]-8}/5=1,
                                                         20-1=19,
                                                   [3], {[(321+1)/2]-18}/7=20,    {20+[(7-1)/2]-2}/3=7,
                                                                                                   {20+[(7-1)/2]-8}/5=3,
                                                         20-(7-3)=16,
                                                   [4], {[(321+1)/2]-50}/11=10, {10+[(11-1)/2]-2}/3=4,
                                                                                                   {10+[(11-1)/2]-8}/5=1,
                                                         10-(4-1)=7
                                                   [4], {[(321+1)/2]-72}/13=6,    {6+[(13-1)/2]-2}/3=3, 6-3=3
                                                   [5], {[(321+1)/2]-128}/17=1,
                                             146-49-19-16-7-3-1=51,
第12步，(5000-648)/37=117,    (117-1)×2+37=269,
                                                   [1], {[(269+1)/2]-2}/3=44,    {[(37+1)/2]-2}/3=5, 44-5=39,
                                                   [2], {[(269+1)/2]-8}/5=25,    {25+[(5-1)/2]-2}/3=8,  25-8=17,
                                                         {[(37+1)/2]-8}/5=2,
                                                         17-2=15,
                                                   [3], {[(269+1)/2]-18}/7=16,    {16+[(7-1)/2]-2}/3=5,
                                                                                                   {16+[(7-1)/2]-8}/5=2,
                                                         16-(5-2)=13,
                                                   [4], {[(269+1)/2]-50}/11=7,    {7+[(11-1)/2]-2}/3=3, 7-3=4，
                                          117-39-15-13-4=46,
第13步，(5000-800)/41=102,    (102-1)×2+41=243,
                                                   [1], {[(243+1)/2]-2}/3=40,    {[(41+1)/2]-2}/3=6, 40-6=34,
                                                   [2], {[(243+1)/2]-8}/5=22,    {22+[(5-1)/2]-2}/3=7,  22-7=15,
                                                         {[(41+1)/2]-8}/5=2,
                                                         15-2=13,
                                                   [3], {[(243+1)/2]-18}/7=14,    {14+[(7-1)/2]-2}/3=5,
                                                                                                   {14+[(7-1)/2]-8}/5=1,
                                                         14-(5-1)=10,
                                                   [4], {[(243+1)/2]-50}/11=6,    {6+[(11-1)/2]-2}/3=3, 6-3=3，
                                          102-34-13-10-3=42,
第14步，(5000-882)/43=95,    (95-1)×2+43=231,
                                                   [1], {[(231+1)/2]-2}/3=38,    {[(43+1)/2]-2}/3=6, 38-6=32,
                                                   [2], {[(231+1)/2]-8}/5=21,    {21+[(5-1)/2]-2}/3=7,  21-7=14,
                                                         {[(43+1)/2]-8}/5=2,
                                                         14-2=12,
                                                   [3], {[(231+1)/2]-18}/7=14,    {14+[(7-1)/2]-2}/3=5,
                                                                                                   {14+[(7-1)/2]-8}/5=1,
                                                         14-(5-1)=10,
                                                   [4], {[(231+1)/2]-50}/11=6,    {6+[(11-1)/2]-2}/3=3, 6-3=3，
                                          95-32-12-10-3=38,
第15步，(5000-1058)/47=83,    (83-1)×2+47=211,
                                                   [1], {[(211+1)/2]-2}/3=34,    {[(47+1)/2]-2}/3=7, 34-7=27,
                                                   [2], {[(211+1)/2]-8}/5=19,    {19+[(5-1)/2]-2}/3=6,  19-6=13,
                                                         {[(47+1)/2]-8}/5=3,       {3+[(5-1)/2]-2}/3=1, 3-1=2,
                                                         13-2=11,
                                                   [3], {[(211+1)/2]-18}/7=12,    {12+[(7-1)/2]-2}/3=4,
                                                                                                   {12+[(7-1)/2]-8}/5=1,
                                                         12-(4-1)=9,
                                                   [4], {[(211+1)/2]-50}/11=5,    {5+[(11-1)/2]-2}/3=2, 5-2=3，
                                          83-27-11-9-3=33,
第16步，(5000-1352)/53=68,    (68-1)×2+59=187,
                                                   [1], {[(187+1)/2]-2}/3=30, {[(53+1)/2]-2}/3=8, 30-8=22,
                                                   [2], {[(187+1)/2]-8}/5=17, {17+[(5-1)/2]-2}/3=5,  17-5=12,
                                                         {[(53+1)/2]-8}/5=3,       {3+[(5-1)/2]-2}/3=1, 3-1=2,
                                                         12-2=10,
                                                   [3], {[(187+1)/2]-18}/7=10,    {10+[(7-1)/2]-2}/3=3, 10-3=7，
                                                         {[(53+1)/2]-18}/7=1,
                                                         7-1=6,
                                                   [4], {[(187+1)/2]-50}/11=4,  {4+[(7-1)/2]-2}/3=1, 4-1=3，
                                          68-22-10-6-3=27,
第17步，(5000-1682)/59=56,    (56-1)×2+59=169,
                                                   [1], {[(169+1)/2]-2}/3=27, {[(59+1)/2]-2}/3=9, 27-9=18,
                                                   [2], {[(169+1)/2]-8}/5=15, {15+[(5-1)/2]-2}/3=5,  15-5=10,
                                                         {[(59+1)/2]-8}/5=4,       {4+[(5-1)/2]-2}/3=1, 4-1=3,
                                                         10-3=7,
                                                   [3], {[(169+1)/2]-18}/7=9,    {9+[(7-1)/2]-2}/3=3, 9-3=6，
                                                         {[(59+1)/2]-18}/7=1,
                                                         6-1=5,
                                                   [4], {[(169+1)/2]-50}/11=3,  {3+[(7-1)/2]-2}/3=1, 3-1=2，
                                          56-18-7-5-2=24,
第18步，(5000-1800)/61=52,    (52-1)×2+61=163,
                                                   [1], {[(163+1)/2]-2}/3=26, {[(61+1)/2]-2}/3=9, 26-9=17,
                                                   [2], {[(163+1)/2]-8}/5=14, {14+[(5-1)/2]-2}/3=4,  14-4=10,
                                                         {[(61+1)/2]-8}/5=4,       {4+[(5-1)/2]-2}/3=1, 4-1=3,
                                                         10-3=7,
                                                   [3], {[(163+1)/2]-18}/7=9,    {9+[(7-1)/2]-2}/3=3, 9-3=6
                                                         {[(61+1)/2]-18}/7=1,
                                                         6-1=5,
                                                   [4], {[(163+1)/2]-50}/11=2,
                                          52-17-7-5-2=21,
第19步，(5000-2178)/67=42,    (42-1)×2+67=149,
                                                   [1], {[(149+1)/2]-2}/3=24, {[(67+1)/2]-2}/3=10, 24-10=14,
                                                   [2], {[(149+1)/2]-8}/5=13, {13+[(5-1)/2]-2}/3=4,  13-4=9,
                                                         {[(67+1)/2]-8}/5=5,       {5+[(5-1)/2]-2}/3=1, 5-1=4,
                                                         9-4=5,
                                                   [3], {[(149+1)/2]-18}/7=8,    {8+[(7-1)/2]-2}/3=3, 8-3=5
                                                         {[(67+1)/2]-18}/7=2,    {2+[(7-1)/2]-2}/3=1, 2-1=1,
                                                         5-1=4,
                                                   [4], {[(149+1)/2]-50}/11=2,
                                          42-14-5-4-2=17,
第20步，(5000-2450)/71=35,    (35-1)×2+71=139,
                                                   [1], {[(139+1)/2]-2}/3=22, {[(71+1)/2]-2}/3=11, 22-11=11,
                                                   [2], {[(139+1)/2]-8}/5=12, {12+[(5-1)/2]-2}/3=4,  12-4=8,
                                                         {[(71+1)/2]-8}/5=5,       {5+[(5-1)/2]-2}/3=1, 5-1=4,
                                                         8-4=4,
                                                   [3], {[(135+1)/2]-18}/7=7,    {7+[(7-1)/2]-2}/3=2, 7-2=5
                                                         {[(71+1)/2]-18}/7=2,    {2+[(7-1)/2]-2}/3=1, 2-1=1,
                                                         5-1=4,
                                                   [4], {[(139+1)/2]-50}/11=1,
                                          35-11-4-4-1=15,
第21步，(5000-2592)/73=32,    (32-1)×2+73=135,
                                                   [1], {[(135+1)/2]-2}/3=22, {[(73+1)/2]-2}/3=11, 22-11=11,
                                                   [2], {[(135+1)/2]-8}/5=12, {12+[(5-1)/2]-2}/3=4,  12-4=8,
                                                         {[(73+1)/2]-8}/5=5,       {5+[(5-1)/2]-2}/3=1, 5-1=4,
                                                         8-4=4,
                                                   [3], {[(135+1)/2]-18}/7=7,    {7+[(7-1)/2]-2}/3=2, 7-2=5
                                                         {[(73+1)/2]-18}/7=2,    {2+[(7-1)/2]-2}/3=1, 2-1=1,
                                                         5-1=4,
                                                   [4], {[(135+1)/2]-50}/11=1,
                                          32-11-4-4-1=12,
第22步，(5000-3042)/79=24,    (24-1)×2+79=125,
                                                   [1], {[(125+1)/2]-2}/3=20, {[(79+1)/2]-2}/3=12, 20-12=8,
                                                   [2], {[(125+1)/2]-8}/5=11, {11+[(5-1)/2]-2}/3=3,  11-3=8,
                                                         {[(79+1)/2]-8}/5=6,       {6+[(5-1)/2]-2}/3=2, 6-2=4,
                                                         8-4=4,
                                                   [3], {[(125+1)/2]-18}/7=6,    {6+[(7-1)/2]-2}/3=2, 6-2=4
                                                         {[(79+1)/2]-18}/7=3,    {3+[(7-1)/2]-2}/3=1, 3-1=2,
                                                         4-2=2,
                                                   [4], {[(125+1)/2]-50}/11=1,
                                          24-8-4-2-1=9,
第23步，(5000-3362)/83=19,    (19-1)×2+83=119,
                                                   [1], {[(119+1)/2]-2}/3=19, {[(83+1)/2]-2}/3=13, 19-13=6,
                                                   [2], {[(119+1)/2]-8}/5=10, {10+[(5-1)/2]-2}/3=3,    10-3=7,
                                                         {[(83+1)/2]-8}/5=6,       {6+[(5-1)/2]-2}/3=2,    6-2=4
                                                         7-4=3
                                                   [3], {[(119+1)/2]-18}/7=6,    {6+[(7-1)/2]-2}/3=2, 6-2=4,
                                                         {[(83+1)/2]-18}/7=3,    {3+[(7-1)/2]-2}/3=1, 3-1=2,
                                                         4-2=2,
                                          19-6-3-2=8,
第24步，(5000-3872)/89=12,    (12-1)×2+89=111,
                                                   [1], {[(111+1)/2]-2}/3=18, {[(89+1)/2]-2}/3=14, 18-14=4,
                                                   [2], {[(111+1)/2]-8}/5=9,    {9+[(5-1)/2]-2}/3=3,    9-3=6,
                                                         {[(89+1)/2]-8}/5=7,       {7+[(5-1)/2]-2}/3=2,    7-2=5
                                                         6-5=1
                                                   [3], {[(111+1)/2]-18}/7=5,    {5+[(7-1)/2]-2}/3=2, 5-2=3,
                                                         {[(89+1)/2]-18}/7=3,    {3+[(7-1)/2]-2}/3=1, 3-1=2,
                                                         3-2=1,
                                          12-4-1-1=6,
第25步，(5000-4608)/97=4,       (4-1)×2+97=103,
                                                   {[(103+1)/2]-2}/3=16,  {[(97+1)/2]-2}/3=15, 16-15=1,
                                          4-1=3,

朱明君 · 发表于 2022-12-4 17:12

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