cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A098680 Primes p whose period of reciprocal equals (p-1)/13.

Original entry on oeis.org

2393, 15497, 18149, 18617, 20021, 25819, 26183, 26339, 29303, 39937, 42953, 48491, 52313, 53327, 57331, 58189, 59021, 65183, 81953, 82499, 87491, 91703, 98047, 102233, 104287, 109097, 111229, 119419, 129793, 131171, 143287, 143833, 162007
Offset: 1

Views

Author

Robert G. Wilson v, Sep 15 2004

Keywords

Links

Crossrefs

Cf. A097443, A055628, A056157, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A135073.

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, 15000]], f[ # ] == 13 &]

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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.

Examples

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

Links

Crossrefs

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

Programs

  • 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 *)

Extensions

Corrected and extended by R. J. Mathar, Feb 21 2008
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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