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Search: id:A119678
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| A119678 |
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a(n) = least k such that the remainder when 4^k is divided by k is n. |
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35
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| 3, 14, 137243, 5, 6821, 10, 57, 124, 35, 18, 2791496231, 244, 51, 505, 199534799, 20, 30271293169, 49, 45, 236, 399531841, 42, 533, 25, 39, 50, 352957, 36, 995, 98, 33, 112, 47503, 55, 42345881, 44, 2981, 289, 805, 78, 1019971289, 25498, 2121, 212
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(5^k-1) = 5^k.
a(n) > n.
Numbers n>1 such that a(n-1) = n are listed in A015950 = {1, 5, 25, 125, 205, 625, 1025, 2525, 3125, ...}
Numbers n such that n | 4^n + 1.
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LINKS
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Ryan Propper, Feb 21 2007, Table of n, a(n) for n = 1..82
Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found
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MATHEMATICA
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Do[k = 1; While[PowerMod[4, k, k] != n, k++ ]; Print[k], {n, 30}]
t = Table[0, {10000} ]; k = 1; While[ k < 5000000000, a = PowerMod[4, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t
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CROSSREFS
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Cf. A015950, A036236, A078457, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.
Sequence in context: A088334 A050645 A048568 this_sequence A096682 A009215 A088558
Adjacent sequences: A119675 A119676 A119677 this_sequence A119679 A119680 A119681
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KEYWORD
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nonn
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Jun 12 2006
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EXTENSIONS
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a(11) <= 2791496231 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007
a(17) <= 140631956671 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 09 2007
a(53) <= 52134328061 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007
a(11) <= 29530730993777374794161795457107 from Max Alekseyev (maxale(AT)gmail.com), Feb 04 2007
a(11) = 2791496231 from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 11 2007. Confirmed by Ryan Propper (rpropper(AT)stanford.edu), Feb 15 2007.
Extended through n = 82 by Ryan Propper (rpropper(AT)stanford.edu), Feb 21 2007
I expanded the search limits in the Mathematica coding Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 14 2009
Link corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 24 2009
a(83) = 3085807457009 = 113 * 331 * 82501603. a(87) > 10^13. [From Hagen von Eitzen (math(AT)von-eitzen.de), Jul 27 2009]
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