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.
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
KEYWORD
base,nonn
AUTHOR
Robert G. Wilson v, Nov 22 2004
EXTENSIONS
More terms from Robert Israel, May 25 2020
STATUS
approved