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Search: id:A135073
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| A135073 |
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Primes for which the period of the reciprocal equals (p-1)/14. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2008, Table of n, a(n) for n = 1..57
Makoto Kamada, Factorizations of 11...11 (Repunit).
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EXAMPLE
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1289 has period of reciprocal 92, or (1289/1)/14.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Feb 21 2008
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CROSSREFS
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Cf. A056217, A056215, A056213, A056211, A056157.
Adjacent sequences: A135070 A135071 A135072 this_sequence A135074 A135075 A135076
Sequence in context: A020466 A142420 A105376 this_sequence A036945 A012169 A093402
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KEYWORD
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nonn
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AUTHOR
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Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2008
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