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A100491 Periodicity of the reciprocal of the Mersenne numbers (A001348). 0
1, 6, 15, 42, 44, 1365, 3855, 74898, 44620, 39672, 195225786 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

"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]

REFERENCES

Keith Ball, Strange Curves, Counting Rabbits and other Mathematical Explorations, Princeton University Press, Princeton and Oxford, 2003, Page 57.

LINKS

Table of n, a(n) for n=1..11.

MATHEMATICA

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}]

CROSSREFS

Cf. A001348.

Sequence in context: A273829 A114696 A106368 * A220030 A230165 A271687

Adjacent sequences:  A100488 A100489 A100490 * A100492 A100493 A100494

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Nov 22 2004

STATUS

approved

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Last modified October 14 17:41 EDT 2019. Contains 328022 sequences. (Running on oeis4.)