A056213 Primes p for which the period of reciprocal = (p-1)/8.

41, 241, 1601, 1609, 2441, 2969, 3041, 3449, 3929, 4001, 4409, 5009, 6089, 6521, 6841, 8161, 8329, 8609, 9001, 9041, 9929, 13001, 13241, 14081, 14929, 16001, 16481, 17489, 17881, 18121, 19001, 20249, 20641, 20921, 21529, 22481, 23801

Offset: 1

Author

Robert G. Wilson v, Aug 02 2000

Keywords

• nonn
• base

Comments

Cyclic numbers of the eighth degree (or eighth order): the reciprocals of these numbers belong to one of eight different cycles. Each cycle has the (number minus 1)/8 digits.

From Robert Israel, Apr 02 2018: (Start)

Primes p such that A002371(A000720(p))=(p-1)/8.

All terms == 1 (mod 8). (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to decimal expansion of 1/n

Programs

Maple

select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/8, [seq(t,t=17..24000,8)]); # 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, 2700]], f[ # ] == 8 &]

Extensions

Edited by N. J. A. Sloane, Apr 30 2007