A100491 Periodicity of the reciprocal of the Mersenne numbers (A001348).

1, 6, 15, 42, 44, 1365, 3855, 74898, 44620, 39672, 195225786, 616318176, 26815350376, 1186422030, 663226400, 1001874900, 4885233465012400, 1152921504606846975, 10197205073773110, 9758202933231640, 2908370863958880, 1152589154156603558, 2895630705663782454386, 103161669940448356241593685

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..24.

Maple

seq(numtheory:-order(10, 2^ithprime(i)-1), i=1..20); # Robert Israel, May 25 2020

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

Extensions

More terms from Robert Israel, May 25 2020

Status

approved