A381923 a(n) is the least k >= 2 such that (2^k - 1) mod (n*k - 1) = 0.

2, 2, 12, 4, 24, 216, 792, 32, 144, 4410, 396, 108, 208, 1880, 3192, 16, 9240, 72, 24, 6048, 264, 2160, 1872, 270, 20916, 104, 5292, 940, 360, 1596, 756, 8, 132, 4620, 1260, 36, 1728, 12, 49500, 3024, 7560, 3168, 1440, 1080, 2688, 936, 1344, 1035, 44100, 28800

Offset: 1

Author

Ctibor O. Zizka, Mar 10 2025

Keywords

• nonn

Comments

a(n) is even if n is odd. - Robert Israel, Mar 12 2025

Examples

			n = 1: (2^k - 1) mod (1*k - 1) = 0 is true for least k = 2, thus a(1) = 2.
n = 3: (2^k - 1) mod (3*k - 1) = 0 is true for least k = 12, thus a(3) = 12.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000225, A081856, A087965.

Programs

Maple

f:= proc(n) local k;
      for k from 2 by (n mod 2 + 1) do if 2 &^k - 1 mod (n*k-1) = 0 then return k fi od
end proc:
map(f, [$1..200]); # Robert Israel, Mar 12 2025

Mathematica

a[n_] := Module[{k = 2}, While[n*k-1 != 1 && PowerMod[2, k, n*k-1] != 1, k++]; k]; Array[a, 50] (* Amiram Eldar, Mar 10 2025 *)

PARI

a(n) = my(k=2); while (Mod(2, n*k-1)^k != 1, k++); k; \\ Michel Marcus, Mar 10 2025