A128159 a(n) = least k such that the remainder when 19^k is divided by k is n.

2, 17, 358, 5, 7, 13, 118, 11, 22, 207, 14, 6683, 21, 1055, 221, 6843, 86, 39959, 23, 559, 34, 129, 26, 25, 51, 799, 334, 33, 166, 47427581, 1537, 901, 68, 39, 326, 87169, 44, 161, 46, 3509, 341, 529, 106, 1098179, 158, 657, 314, 49621349, 75, 143, 62, 749, 116

Offset: 1

Author

Alexander Adamchuk, Feb 16 2007

Keywords

• hard
• nonn

Comments

a(447) = 7987803178, a(660) = 11147676413, a(923) = 6246715274. - Daniel Morel, Jun 08 2010

a(216) = 21686254249, a(296) = 40778012377, a(386) = 15891209603, a(582) = 46530896443, a(638) = 15297472657, a(736) = 45211411479, a(872) = 106458212591. - Daniel Morel, Oct 15 2010

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128160.

Cf. A128149, A128150.

Programs

Mathematica

t = Table[0, {10000} ]; k = 1; While[ k < 3100000000, a = PowerMod[19, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)
clk=Compile[{{n,Integer}},{k=1};While[PowerMod[19,k,k]!=n,k++];k]; Array[ clk,55] (* _Harvey P. Dale, May 10 2014 *)

Extensions

More terms from Ryan Propper, Mar 24 2007

More terms from Robert G. Wilson v, Aug 04 2009