A135073 Primes for which the period of the reciprocal equals (p-1)/14.

449, 1289, 3557, 4397, 4999, 5209, 6203, 6637, 7043, 8387, 10613, 11369, 13147, 13399, 14323, 16871, 18481, 19391, 20147, 20707, 26489, 28813, 29387, 29947, 30241, 32831, 32999, 33587, 36107, 37591, 38053, 39719, 40559, 41231, 41609

Offset

1,1

Comments

Also cyclic numbers of the fourteenth degree (or fourteenth order): the reciprocals of these numbers belong to one of fourteen different cycles. Each cycle has the (number minus 1)/14 digits.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..57 from R. J. Mathar, Feb 21 2008)

Makoto Kamada, Factorizations of 11...11 (Repunit).

Example

1289 has period of reciprocal 92, or (1289/1)/14.

Maple

A007732 := proc(n) local nred25 ; nred25 := n ; while nred25 mod 2 = 0 and nred25 > 1 do nred25 := nred25/2 ; od; while nred25 mod 5 = 0 and nred25 > 1 do nred25 := nred25/5 ; od; if nred25 = 1 then 1; else numtheory[order](10, nred25) ; fi ; end: for n from 1 to 22000 do p := ithprime(n) ; if 14*A007732(p) = p-1 then printf("%d, ", p) ; fi ; od: # R. J. Mathar, Feb 21 2008

Mathematica

Select[Prime[Range[4500]], Length[RealDigits[1/#][[1, 1]]]==(#-1)/14&] (* Harvey P. Dale, Jun 22 2013 *)

Crossrefs

Cf. A097443, A055628, A056157, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680.

Sequence in context: A105376 A325083 A243402 * A160291 A193255 A283791

Adjacent sequences: A135070 A135071 A135072 * A135074 A135075 A135076

Keyword

nonn,base

Author

Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008

Extensions

Corrected and extended by R. J. Mathar, Feb 21 2008

Status

approved