A056217 Primes p for which the period of reciprocal 1/p is (p-1)/12.

37, 613, 733, 1597, 2677, 3037, 4957, 5197, 5641, 7129, 7333, 7573, 8521, 8677, 11317, 14281, 14293, 15289, 15373, 16249, 17053, 17293, 17317, 19441, 20161, 21397, 21613, 21997, 23053, 23197, 24133, 25357, 25717, 26053, 26293, 27277

Offset: 1

Author

Robert G. Wilson v, Aug 02 2000

Keywords

• nonn
• base

Comments

Cyclic numbers of the twelfth degree (or twelfth order): the reciprocals of these numbers belong to one of twelve different cycles. Each cycle has the (number minus 1)/12 digits.

Primes p such that the order of 2 mod p is (p-1)/12. - Robert Israel, Dec 08 2017

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(p -> isprime(p) and numtheory:-order(10, p) = (p-1)/12, [seq(i,i=13..30000,12)]); # Robert Israel, Dec 08 2017

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, 3000]], f[ # ] == 12 &]