A056210 Primes p whose period of reciprocal equals (p-1)/5.

11, 251, 1061, 1451, 1901, 1931, 2381, 3181, 3491, 3851, 4621, 4861, 5261, 6101, 6491, 6581, 6781, 7331, 8101, 9941, 10331, 10771, 11251, 11261, 11411, 12301, 14051, 14221, 14411, 15091, 15131, 16061, 16141, 16301, 16651, 16811, 16901

Offset: 1

Author

Robert G. Wilson v, Aug 02 2000

Keywords

• nonn
• base

Comments

Cyclic numbers of the fifth degree (or fifth order): the reciprocals of these numbers belong to one of five different cycles. Each cycle has the (number minus 1)/5 digits.

From Robert Israel, Apr 02 2018: (Start)

Primes p such that A002371(A000720(p)) = (p-1)/5.

All terms == 1 (mod 10). (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Index entries for sequences related to decimal expansion of 1/n

Crossrefs

Cf. A000720, A001913, A002371, A097443, A055628, A056157, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680.

Programs

Maple

select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/5, [seq(t,t=11..17000,10)]); # Robert Israel, Apr 02 2018

Mathematica

f[n_Integer] := Block[{ds = Divisors[n - 1]}, (n - 1)/Take[ ds, Position[ PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ -1]]]; Select[ Prime[ Range[4, 2000]], f[ # ] == 5 &]

Extensions

Entry revised by N. J. A. Sloane, Apr 30 2007