A015922 Numbers k such that 2^k == 8 (mod k).

1, 2, 3, 4, 8, 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 248, 249, 267, 291, 303, 309, 315, 321, 327, 339, 381, 393, 399, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

For all m, 2^A015921(m) - 1 belongs to this sequence.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..29055 (first 6822 terms from Zak Seidov)
• OEIS Wiki, 2^n mod n.

Crossrefs

Contains A033553 as a subsequence.

The odd terms form A276967.

Cf. A015921, A130133, A130134.

Programs

Mathematica

a015922Q[n_Integer] := If[Mod[2^n, n] == Mod[8, n], True, False];
a015922[n_Integer] :=
Flatten[Position[Thread[a015922Q[Range[n]]], True]];
a015922[1000000] (* Michael De Vlieger, Jul 16 2014 *)
m = 8; Join[Select[Range[m], Divisible[2^# - m, #] &], Select[Range[m + 1, 10^3], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)
Join[{1,2,3,4,8},Select[Range[650],PowerMod[2,#,#]==8&]] (* Harvey P. Dale, Aug 22 2020 *)

PARI

isok(n) = Mod(2, n)^n == Mod(8, n); \\ Michel Marcus, Oct 13 2013, Jul 16 2014

Extensions

First 5 terms inserted by David W. Wilson