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A056213 Primes p for which the period of reciprocal = (p-1)/8. 4

%I

%S 41,241,1601,1609,2441,2969,3041,3449,3929,4001,4409,5009,6089,6521,

%T 6841,8161,8329,8609,9001,9041,9929,13001,13241,14081,14929,16001,

%U 16481,17489,17881,18121,19001,20249,20641,20921,21529,22481,23801

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

%C 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.

%C From _Robert Israel_, Apr 02 2018: (Start)

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

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

%H Robert Israel, <a href="/A056213/b056213.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%p select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/8, [seq(t,t=17..24000,8)]); # _Robert Israel_, Apr 02 2018

%t 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 &]

%K nonn,base

%O 1,1

%A _Robert G. Wilson v_, Aug 02 2000

%E Edited by _N. J. A. Sloane_, Apr 30 2007

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Last modified July 13 05:18 EDT 2020. Contains 335673 sequences. (Running on oeis4.)