Magic constant: Difference between revisions
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10^20 5848036 |
10^20 5848036 |
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</pre> |
</pre> |
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=={{header|Mathematica}}/{{header|Wolfram Language}}== |
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<lang Mathematica>ClearAll[i, n, MagicSumHelper, MagicSum, InverseMagicSum] |
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MagicSumHelper[n_] = Sum[i, {i, n^2}]/n; |
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MagicSum[n_] := MagicSumHelper[n + 2] |
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InverseMagicSum[lim_] := Ceiling[-(1/(3^(1/3) (9 lim + Sqrt[3] Sqrt[1 + 27 lim^2])^(1/3))) + (9 lim + Sqrt[3] Sqrt[1 + 27 lim^2])^(1/3)/3^(2/3)] |
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MagicSum /@ Range[20] |
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MagicSum[1000] |
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exps = Range[1, 50]; |
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nums = 10^exps; |
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Transpose[{Superscript[10, #] & /@ exps, InverseMagicSum[nums]}] // Grid</lang> |
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{{out}} |
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<pre>{15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, 2465, 2925, 3439, 4010, 4641, 5335} |
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503006505 |
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10^1 3 |
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10^2 6 |
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10^3 13 |
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10^4 28 |
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10^5 59 |
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10^6 126 |
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10^7 272 |
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10^8 585 |
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10^9 1260 |
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10^10 2715 |
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10^11 5849 |
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10^12 12600 |
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10^13 27145 |
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10^14 58481 |
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10^15 125993 |
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10^16 271442 |
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10^17 584804 |
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10^18 1259922 |
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10^19 2714418 |
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10^20 5848036 |
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10^21 12599211 |
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10^22 27144177 |
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10^23 58480355 |
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10^24 125992105 |
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10^25 271441762 |
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10^26 584803548 |
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10^27 1259921050 |
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10^28 2714417617 |
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10^29 5848035477 |
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10^30 12599210499 |
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10^31 27144176166 |
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10^32 58480354765 |
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10^33 125992104990 |
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10^34 271441761660 |
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10^35 584803547643 |
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10^36 1259921049895 |
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10^37 2714417616595 |
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10^38 5848035476426 |
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10^39 12599210498949 |
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10^40 27144176165950 |
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10^41 58480354764258 |
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10^42 125992104989488 |
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10^43 271441761659491 |
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10^44 584803547642574 |
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10^45 1259921049894874 |
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10^46 2714417616594907 |
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10^47 5848035476425733 |
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10^48 12599210498948732 |
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10^49 27144176165949066 |
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10^50 58480354764257322</pre> |
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=={{header|Perl}}== |
=={{header|Perl}}== |