A119679 a(n) = least k such that the remainder when 5^k is divided by k is n.

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

Offset: 1

Author

Ryan Propper, Jun 12 2006

Keywords

• nonn

Comments

From Alexander Adamchuk, Jan 31 2007: (Start)

a(n) > n.

For numbers n such that a(n-1) = n, see A015951 except first term. (End)

a(58) <= 16860204577843069 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007

Links

• 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v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found [This file is now out of date - see the extension lines below.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]

Crossrefs

Cf. A015951, A036236, A078457, A119678, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

Programs

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 (* changed (to reflect the new limits) by Robert G. Wilson v, Jul 14 2009 *)

Extensions

Revised by Max Alekseyev, Sep 25 2007

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