This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375792 #13 Aug 29 2024 12:53:24 %S A375792 3,11,131,4091,5851,17291,283051,289771,346963,1008547,1082971, %T A375792 3424651,3919771,6464611,6852691,7298131,7514851,8733691,12752251, %U A375792 16740371,17227891,19895611,27393211,30281371,33875323,40528531,45744931,68174107,81011971,98940403 %N A375792 Numbers k such that 2^k == 2 (mod k-th triangular number) and not 2^k == 2 (mod k-th oblong number). %C A375792 Conjecture: all terms of the sequence are prime numbers A000040. %C A375792 The conjecture is false: 45812984491 = 1777 * 25781083 is in the sequence. - _Charles R Greathouse IV_, Aug 29 2024 %o A375792 (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]; %o A375792 (PARI) is(n)=my(m=n*(n+1)); Mod(2,m)^n==m/2+2 \\ _Charles R Greathouse IV_, Aug 29 2024 %Y A375792 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. %K A375792 nonn %O A375792 1,1 %A A375792 _Juri-Stepan Gerasimov_, Aug 29 2024 %E A375792 a(19)-a(30) from _Charles R Greathouse IV_, Aug 29 2024