A375792 Numbers k such that 2^k == 2 (mod k-th triangular number) and not 2^k == 2 (mod k-th oblong number).

3, 11, 131, 4091, 5851, 17291, 283051, 289771, 346963, 1008547, 1082971, 3424651, 3919771, 6464611, 6852691, 7298131, 7514851, 8733691, 12752251, 16740371, 17227891, 19895611, 27393211, 30281371, 33875323, 40528531, 45744931, 68174107, 81011971, 98940403

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 29 2024

Keywords

• nonn

Comments

Conjecture: all terms of the sequence are prime numbers A000040.

The conjecture is false: 45812984491 = 1777 * 25781083 is in the sequence. - Charles R Greathouse IV, Aug 29 2024

Crossrefs

Cf. A000217 (triangular numbers), A002378 (oblong numbers), A216822 (n such that 2^n == 2 (mod n*(n+1))), A375793 (n such that 2^n == 2 (mod n*(n+1) div 2)), A217465.

Programs

Magma

[n: n in [1..10^5] | 2^n mod (n*(n+1) div 2) eq 2 and not 2^n mod (n*(n+1)) eq 2];

PARI

is(n)=my(m=n*(n+1)); Mod(2,m)^n==m/2+2 \\ Charles R Greathouse IV, Aug 29 2024

Extensions

a(19)-a(30) from Charles R Greathouse IV, Aug 29 2024