A375794 Numbers k such that 2^k == 2 (mod ((k - 1)*k/2)) and not 2^k == 2 (mod ((k - 1)*k)).

5, 13, 37, 61, 101, 109, 157, 181, 421, 541, 661, 757, 821, 1093, 1621, 1861, 2029, 2053, 2269, 2341, 2437, 2701, 2917, 3277, 3301, 3613, 4621, 4789, 4861, 5461, 5501, 5581, 6301, 6661, 7309, 8101, 8269, 8581, 8821, 8893, 9829, 9901, 10141, 10261, 10501, 10837, 11701, 12101, 12301

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 29 2024

Keywords

• nonn

Comments

a(22) = 2701 is the first composite term of the sequence.

Crossrefs

Cf. A069051, A375792.

Programs

Magma

[k: k in [2..13333] | Modexp(2, k, (k^2-k) div 2) eq 2 and not Modexp(2, k, k^2-k) eq 2];

Mathematica

Select[Range[2,12400], PowerMod[2,#,(#-1)#/2]==2 && !PowerMod[2,#,(#-1)#]==2 &] (* Stefano Spezia, Sep 19 2024 *)

PARI

isok(k)={k > 1 && Mod(2, (k-1)*k)^k == 2 + (k-1)*k/2} \\ Andrew Howroyd, Aug 29 2024