A056157 Primes p whose period of reciprocal equals (p-1)/4.

53, 173, 277, 317, 397, 769, 773, 797, 809, 853, 1009, 1013, 1093, 1493, 1613, 1637, 1693, 1721, 2129, 2213, 2333, 2477, 2521, 2557, 2729, 2797, 2837, 3329, 3373, 3517, 3637, 3733, 3797, 3853, 3877, 4133, 4241, 4253, 4373, 4493, 4729, 4733, 4877, 5081

Offset: 1

Author

Don Willard (dwillard(AT)prairie.cc.il.us), Jun 05 2000

Keywords

• nonn
• base

Comments

Cyclic numbers of the fourth degree (or fourth order): the reciprocals of these numbers belong to one of four different cycles. Each cycle has the (number minus 1)/4 digits.

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. A001913, A097443, A055628, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680.

Programs

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, 700]], f[ # ] == 4 &] (* Robert G. Wilson v, Aug 02 2000 *)
LP[ n_Integer ] := (ds = Divisors[ n - 1 ]; Take[ ds, Position[ PowerMod[ 10, ds, n ], 1 ][ [ 1, 1 ] ] ][ [ -1 ] ]); CL[ n_Integer ] := (n - 1)/LP[ n ]; Select[ Range[ 7, 7500 ], PrimeQ[ # ] && CL[ # ] == 4 & ] (* Robert G. Wilson v, Aug 02 2000 *)

Extensions

More terms from Robert G. Wilson v, Aug 02 2000