A081116 Numbers k such that 17 divides 3^k-k.

5, 29, 42, 75, 132, 134, 140, 152, 159, 162, 163, 201, 206, 215, 241, 256, 277, 301, 314, 347, 404, 406, 412, 424, 431, 434, 435, 473, 478, 487, 513, 528, 549, 573, 586, 619, 676, 678, 684, 696, 703, 706, 707, 745, 750, 759, 785, 800, 821, 845, 858, 891, 948

Offset: 1

Author

Benoit Cloitre, Apr 16 2003

Keywords

• nonn

Comments

Suggested by a problem in a web page by Hojoo Lee entitled "Challenging problems in number theory". However, the page no longer exists.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

Crossrefs

Cf. A024024 (3^n-n).

Programs

Mathematica

Select[Range[1000], PowerMod[3, #, 17] == Mod[#, 17] &] (* Amiram Eldar, May 14 2022 *)

PARI

isok(n) = Mod(3, 17)^n == Mod(n, 17); \\ Michel Marcus, Dec 02 2013

Formula

a(n+1)-a(n) is the 16-periodic sequence (24, 13, 33, 57, 2, 6, 12, 7, 3, 1, 38, 5, 9, 26, 15, 21).