A276967 Odd integers n such that 2^n == 2^3 (mod n).

1, 3, 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 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, 669, 681, 687, 693, 699, 717, 723, 731, 753, 771, 789, 807

Offset: 1

Author

Max Alekseyev, Sep 22 2016

Keywords

• nonn
• easy

Comments

Also, integers n such that 2^(n - 3) == 1 (mod n).

Contains A033553 as a subsequence. Smallest term greater than 3 missing in A033553 is 731.

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

The odd terms of A015922.

Odd integers n such that 2^n == 2^k (mod n): A176997 (k = 1), A173572 (k = 2), this sequence (k = 3), A033984 (k = 4), A276968 (k = 5), A215610 (k = 6), A276969 (k = 7), A215611 (k = 8), A276970 (k = 9), A215612 (k = 10), A276971 (k = 11), A215613 (k = 12).

Programs

Mathematica

Join[{1}, Select[Range[1, 1023, 2], PowerMod[2, # - 3, #] == 1 &]] (* Alonso del Arte, Sep 22 2016 *)

PARI

isok(n) = (n % 2) && (Mod(2,n)^n==8); \\ Michel Marcus, Sep 23 2016