A307625 Numbers k such that q = 2^k - 2^m + 1 is prime, where m = A270096(k).

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 22, 31, 39, 45, 61, 76, 89, 94, 100, 102, 107, 122, 127, 294, 360, 430, 460, 521, 607, 639, 694, 732, 737, 952, 1279, 1581, 1983, 2061, 2203, 2281, 2319, 2410, 2530, 3217, 4253, 4423, 5324, 6846, 7011, 9615, 9689, 9904, 9941, 10841, 11213

Offset

1,2

Comments

All primes in the sequence are the Mersenne exponents A000043.

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

Links

Table of n, a(n) for n=1..59.

Formula

q == 1 (mod k).

Mathematica

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 *)

Prog

(PARI) f(n) = {my(m = 0); while (Mod(2, n)^m != 2^n, m++); m; } \\ A270096
isok(n) = my(m = f(n)); isprime(2^n - 2^m + 1); \\ Michel Marcus, Apr 23 2019

Crossrefs

Cf. A000043, A270096, A270427, A307590.

Sequence in context: A080571 A165805 A319975 * A165722 A082400 A072993

Adjacent sequences: A307622 A307623 A307624 * A307626 A307627 A307628

Keyword

nonn

Author

Thomas Ordowski, Apr 19 2019

Extensions

More terms from Amiram Eldar, Apr 19 2019

Status

approved