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

1,1

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

Links

Table of n, a(n) for n=1..30.

Prog

(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

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.

Sequence in context: A201611 A088075 A088076 * A276258 A284604 A072878

Adjacent sequences: A375789 A375790 A375791 * A375793 A375794 A375795

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 29 2024

Extensions

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

Status

approved