A127817 a(n) = least k such that the remainder when 9^k is divided by k is n.

2, 7, 6, 5, 38, 723, 74, 2592842671511, 11, 3827, 14, 717, 34, 59035, 21, 259, 152, 237, 62, 626131, 30, 169, 58, 25, 56, 1921, 39, 361, 65, 49, 63010, 287, 48, 55, 46, 63, 932, 3786791, 69, 69637, 230, 221, 6707, 1057, 57, 4907, 253, 681, 148, 393217991, 70

Offset: 1

Author

Alexander Adamchuk, Jan 30 2007

Keywords

• hard
• nonn

Examples

			For n=4, since 9^5 == 4 (mod 5) and 9^k is not congruent to 4 (mod k) for any k < 5, a(4) = 5. _Michael B. Porter_, Dec 10 2016
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found, Nov 21 2016 [With 202 new terms, this supersedes an earlier table of Robert G. Wilson v et al.]

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127818, A127819, A127820, A127821.

Programs

Maple

a127817 := [seq(0,j=1..nmax)] ; for k from 1 do n := modp(9^k,k) ; if n > 0 and n <= nmax then if op(n,a127817) = 0 then a127817 := subsop(n=k,a127817) ; print( op(1..50,a127817) ) ; fi; fi; od: # R. J. Mathar, Jul 16 2009

Mathematica

t = Table[0, {10000}]; k = 1; lst = {}; While[k < 4500000000, a = PowerMod[9, k, k]; If[ a<10001 && t[[a]]==0, t[[a]]=k; Print[{a,k}]]; k++ ]; t

Extensions

a(8) <= 2592842671511 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007

I changed the Mathematica coding to reflect the current limits Robert G. Wilson v, Jul 18 2009

Value for a(8) as suggested by J. K. Crump confirmed by Hagen von Eitzen, Jul 21 2009

Authorship of a-file corrected by R. J. Mathar, Aug 24 2009