A307625 - OEIS

%I #22 Jul 25 2021 01:30:54

%S 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 107,122,127,294,360,430,460,521,607,639,694,732,737,952,1279,1581,

%U 1983,2061,2203,2281,2319,2410,2530,3217,4253,4423,5324,6846,7011,9615,9689,9904,9941,10841,11213

%N Numbers k such that q = 2^k - 2^m + 1 is prime, where m = A270096(k).

%C All primes in the sequence are the Mersenne exponents A000043.

%C It seems that the composite terms are composite numbers k <> 8 such that A307590(k) = 2.

%F q == 1 (mod k).

%t 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 (PARI) f(n) = {my(m = 0); while (Mod(2, n)^m != 2^n, m++); m; } \\ A270096

%o isok(n) = my(m = f(n)); isprime(2^n - 2^m + 1); \\ _Michel Marcus_, Apr 23 2019

%Y Cf. A000043, A270096, A270427, A307590.

%K nonn

%O 1,2

%A _Thomas Ordowski_, Apr 19 2019

%E More terms from _Amiram Eldar_, Apr 19 2019