

A119679


a(n) = least k such that the remainder when 5^k is divided by k is n.


46



2, 3, 22, 4769, 7, 15853, 114, 9, 28, 35, 14, 1328467, 68, 111, 1555, 9569200211, 76, 2030227, 49, 21, 299, 1097122717, 51, 546707, 26, 27, 121, 529, 596, 3095, 138, 93, 136, 34723, 45, 589, 198, 87, 18142961, 595, 292, 319, 318, 117, 55, 20485243, 91
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OFFSET

1,1


COMMENTS

Comments from Alexander Adamchuk, Jan 31 2007: (Start)
a(n) > n.
Numbers n>1 such that a(n1) = n are listed in A015951 = {1, 2, 3, 9, 21, 26, 27, 63, 81, ...} Numbers n such that n  5^n + 1.


LINKS

Table of n, a(n) for n=1..47.
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v, Table of n, a(n) for n = 1..10000 with 1 for those entries where a(n) has not yet been found [This file is now out of date  see the extension lines below.  N. J. A. Sloane, May 22 2010]


MATHEMATICA

Do[k = 1; While[PowerMod[5, k, k] != n, k++ ]; Print[k], {n, 30}]
Table[0, {10000}]; k = 1; lst = {}; While[k < 5000000000, a = PowerMod[5, k, k]; If[ a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t


CROSSREFS

Cf. A015951, A036236, A078457, A119678, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.
Sequence in context: A153256 A137077 A046965 * A191648 A130846 A114101
Adjacent sequences: A119676 A119677 A119678 * A119680 A119681 A119682


KEYWORD

nonn


AUTHOR

Ryan Propper, Jun 12 2006


EXTENSIONS

a(58) <= 16860204577843069 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007
Revised by Max Alekseyev, Sep 25 2007
I changed the Mathematica coding to reflect the new limit. I also took out all of the comment lines which are now in the a119679.txt text file.  Robert G. Wilson v, Jul 14 2009
a(172) = 26598818717 = 23 * 593 * 1039 * 1877, a(288) = 9158745413 = 241 * 347 * 109519, a(518) = 33288260241 = 3 * 43 * 258048529, a(558) = 7722115807 = 7 * 157 * 7026493. [From Daniel Morel, May 18 2010]
a(848) = 6672480963 = 3 * 241 * 9228881 [From Daniel Morel, May 26 2010]
a(416) = 10545901269 [From Daniel Morel, Jul 05 2010]
a(948) = 146246024857 [From Daniel Morel, Jul 12 2010]
a(822) = 466661006683 [From Daniel Morel, Aug 24 2010]


STATUS

approved



