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Search: id:A056157
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| A056157 |
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Primes p for which the period of reciprocal = (p-1)/4. |
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+0
9
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to decimal expansion of 1/n
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MATHEMATICA
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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 (rgwv(AT)rgwv.com)
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 (rgwv(AT)rgwv.com)
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CROSSREFS
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Cf. A001913, A097443, A055628, A056210-A056217, A098680
Adjacent sequences: A056154 A056155 A056156 this_sequence A056158 A056159 A056160
Sequence in context: A142698 A056209 A098671 this_sequence A142919 A142949 A061664
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KEYWORD
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nonn
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AUTHOR
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Don Willard (dwillard(AT)prairie.cc.il.us), Jun 05 2000
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 02 2000
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