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楼主 |
发表于 2024-2-24 07:05:11
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本帖最后由 王守恩 于 2024-2-24 07:39 编辑
数字串(1)极限性价比(数码和: 数位)=33:4。
数字串(2)极限性价比(数码和: 数位)=33:4。
数字串(3)性价比(数码和: 数位)好像就差多了。
- 数字串(1)。Table[k = 6*10^(2 n) - (5*10^n + 1)/3; {k, k^2}, {n, 20}] // TableForm
复制代码
{"583", "339889"},
{"59833", "3579987889"},
{"5998333", "35979998778889"},
{"599983333", "359979999877788889"},
{"59999833333", "3599979999987777888889"},
{"5999998333333", "35999979999998777778888889"},
{"599999983333333", "359999979999999877777788888889"},
{"59999999833333333", "3599999979999999987777777888888889"},
{"5999999998333333333", "35999999979999999998777777778888888889"},
{"599999999983333333333", "359999999979999999999877777777788888888889"},
{"59999999999833333333333", "3599999999979999999999987777777777888888888889"},
{"5999999999998333333333333", "35999999999979999999999998777777777778888888888889"},
{"599999999999983333333333333", "359999999999979999999999999877777777777788888888888889"},
{"59999999999999833333333333333", "3599999999999979999999999999987777777777777888888888888889"},
{"5999999999999998333333333333333", "35999999999999979999999999999998777777777777778888888888888889"},
{"599999999999999983333333333333333", "359999999999999979999999999999999877777777777777788888888888888889"},
{"59999999999999999833333333333333333", "3599999999999999979999999999999999987777777777777777888888888888888889"},
{"5999999999999999998333333333333333333", "35999999999999999979999999999999999998777777777777777778888888888888888889"},
{"599999999999999999983333333333333333333", "359999999999999999979999999999999999999877777777777777777788888888888888888889"},
{"59999999999999999999833333333333333333333", "3599999999999999999979999999999999999999987777777777777777777888888888888888888889"}
- 数字串(2)。Table[k = 3*10^(2 n - 1) - (5*10^n + 19)/3; {k, k^2}, {n, 20}] // TableForm
复制代码
{"7", "49"},
{"2827", "7991929"},
{"298327", "88998998929"},
{"29983327", "898999897988929"},
{"2999833327", "8998999989779888929"},
{"299998333327", "89998999998977798888929"},
{"29999983333327", "899998999999897777988888929"},
{"2999999833333327", "8999998999999989777779888888929"},
{"299999998333333327", "89999998999999998977777798888888929"},
{"29999999983333333327", "899999998999999999897777777988888888929"},
{"2999999999833333333327", "8999999998999999999989777777779888888888929"},
{"299999999998333333333327", "89999999998999999999998977777777798888888888929"},
{"29999999999983333333333327", "899999999998999999999999897777777777988888888888929"},
{"2999999999999833333333333327", "8999999999998999999999999989777777777779888888888888929"},
{"299999999999998333333333333327", "89999999999998999999999999998977777777777798888888888888929"},
{"29999999999999983333333333333327", "899999999999998999999999999999897777777777777988888888888888929"},
{"2999999999999999833333333333333327", "8999999999999998999999999999999989777777777777779888888888888888929"},
{"299999999999999998333333333333333327", "89999999999999998999999999999999998977777777777777798888888888888888929"},
{"29999999999999999983333333333333333327", "899999999999999998999999999999999999897777777777777777988888888888888888929"},
{"2999999999999999999833333333333333333327", "8999999999999999998999999999999999999989777777777777777779888888888888888888929"}
- 数字串(3)。Table[{Floor@Sqrt[10^(2 n - 1)], Floor[Sqrt[10^(2 n - 1)]]^2}, {n, 20}] // TableForm
复制代码
{"3", "9"},
{"31", "961"},
{"316", "99856"},
{"3162", "9998244"},
{"31622", "999950884"},
{"316227", "99999515529"},
{"3162277", "9999995824729"},
{"31622776", "999999961946176"},
{"316227766", "99999999989350756"},
{"3162277660", "9999999998935075600"},
{"31622776601", "999999999956753113201"},
{"316227766016", "99999999999470044512256"},
{"3162277660168", "9999999999997600893788224"},
{"31622776601683", "999999999999949826038432489"},
{"316227766016837", "99999999999999409792567484569"},
{"3162277660168379", "9999999999999997900254631487641"},
{"31622776601683793", "999999999999999979762122758866849"},
{"316227766016837933", "99999999999999999873578871987712489"},
{"3162277660168379331", "9999999999999999993682442519108007561"},
{"31622776601683793319", "999999999999999999937454230741109035761"},
{"316227766016837933199", "99999999999999999999437522862413986373601"},
{"3162277660168379331998", "9999999999999999999994348728804092706672004"},
{"31622776601683793319988", "999999999999999999999940837306036211360320144"},
{"316227766016837933199889", "99999999999999999999999775830391924218829612321"},
{"3162277660168379331998893", "9999999999999999999999996556705153432158953225449"},
{"31622776601683793319988935", "999999999999999999999999971898281360053828522434225"},
{"316227766016837933199889354", "99999999999999999999999999719650264140086317842537316"},
{"3162277660168379331998893544", "9999999999999999999999999997263247695355666440244879936"},
{"31622776601683793319988935444", "999999999999999999999999999979306982349036990584399477136"},
{"316227766016837933199889354443", "99999999999999999999999999999828064831004726657639283840249"}
目标很明确: T(n)应该从A067179中突围出来。
显然: T(44)=893241282627485818275387^2=797879988989995997899989877988999997998969999769=44*9/48=33/4
这是极限性价比(数码和: 数位)了吗?!
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