A015911 Numbers k such that 2^k mod k is odd.

25, 45, 55, 91, 95, 99, 125, 135, 143, 153, 155, 161, 175, 187, 225, 235, 245, 247, 261, 273, 275, 279, 285, 289, 297, 319, 329, 333, 335, 355, 363, 369, 387, 391, 403, 407, 413, 423, 425, 429, 435, 437, 441, 459, 473, 477, 481, 483, 493, 507, 517, 525, 529

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

All terms are composite: due to Fermat's little theorem, 2^p == 2 (mod p) when p is prime. - M. F. Hasler, May 10 2021

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Wikipedia, Fermat's little theorem.

Crossrefs

Cf. A015910, A226221.

Programs

Maple

q:= n-> is(2&^n mod n, odd):
select(q, [$1..1000])[];  # Alois P. Heinz, May 10 2021

Mathematica

Select[Range@532, OddQ@PowerMod[2, #, # ] &]

PARI

is(n)=lift(Mod(2,n)^n)%2 \\ Charles R Greathouse IV, May 31 2013