cp's OEIS Frontend

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.

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

Original entry on oeis.org

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

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Author

Thomas Ordowski, Apr 19 2019

Keywords

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.

Crossrefs

Programs

  • 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 *)
  • 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

Formula

q == 1 (mod k).

Extensions

More terms from Amiram Eldar, Apr 19 2019