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Search: id:A100491
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| A100491 |
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Periodicity of the reciprocal of the Mersenne numbers (A001348). |
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+0
1
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| 1, 6, 15, 42, 44, 1365, 3855, 74898, 44620, 39672, 195225786
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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"The answer to the second question, as to whether there is a point beyond which all primes yield periods shorter than p-1, is unknown. It is widely believed that there should be infinitely many primes for which the period is exactly p-1, but at present we cannot be certain." [Ball]
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REFERENCES
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Keith Ball, Strange Curves, Counting Rabbits, and other Mathematical Explorations, Princeton University Press, Princeton and Oxford, 2003, Page 57.
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MATHEMATICA
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f[n_] := Block[{ds = Divisors[n - 1]}, p = Position[ PowerMod[10, ds, n], 1]; If[p == {}, Length[ RealDigits[1/n][[1, 1]]], Take[ds, p[[1, 1]]][[ -1]]]]; Table[ f[2^Prime[n] - 1], {n, 11}]
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CROSSREFS
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Cf. A001348.
Adjacent sequences: A100488 A100489 A100490 this_sequence A100492 A100493 A100494
Sequence in context: A083011 A114696 A106368 this_sequence A117961 A095122 A082637
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KEYWORD
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base,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 22 2004
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