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 A307625 #22 Jul 25 2021 01:30:54 %S A307625 1,2,3,4,5,6,7,10,12,13,14,16,17,19,22,31,39,45,61,76,89,94,100,102, %T A307625 107,122,127,294,360,430,460,521,607,639,694,732,737,952,1279,1581, %U A307625 1983,2061,2203,2281,2319,2410,2530,3217,4253,4423,5324,6846,7011,9615,9689,9904,9941,10841,11213 %N A307625 Numbers k such that q = 2^k - 2^m + 1 is prime, where m = A270096(k). %C A307625 All primes in the sequence are the Mersenne exponents A000043. %C A307625 It seems that the composite terms are composite numbers k <> 8 such that A307590(k) = 2. %F A307625 q == 1 (mod k). %t A307625 b[n_] := Module[{k = 0}, While[PowerMod[2, n, n] != PowerMod[2, k, n], k++]; k]; aQ[n_] := PrimeQ[2^n - 2^b[n] + 1]; Select[Range[5000], aQ] (* _Amiram Eldar_, Apr 19 2019 *) %o A307625 (PARI) f(n) = {my(m = 0); while (Mod(2, n)^m != 2^n, m++); m; } \\ A270096 %o A307625 isok(n) = my(m = f(n)); isprime(2^n - 2^m + 1); \\ _Michel Marcus_, Apr 23 2019 %Y A307625 Cf. A000043, A270096, A270427, A307590. %K A307625 nonn %O A307625 1,2 %A A307625 _Thomas Ordowski_, Apr 19 2019 %E A307625 More terms from _Amiram Eldar_, Apr 19 2019