A226216 Primes p such that (p-1)/ord(2,p) > (q-1)/ord(2,q) for odd primes q < p.

3, 7, 31, 73, 127, 601, 683, 1103, 1801, 2731, 5419, 8191, 43691, 61681, 65537, 121369, 122921, 131071, 178481, 262657, 524287, 2099863, 2796203, 6700417, 10567201, 13264529, 20394401, 48544121, 97685839, 112901153, 160465489, 164511353, 420778751, 536903681, 616318177

Offset

1,1

Comments

Essentially records in A001917. Sequence is infinite.

The Mersenne primes (A000668) are a subset. - Jeppe Stig Nielsen, Aug 30 2015

Links

Amiram Eldar, Table of n, a(n) for n = 1..47

Formula

a(n) = prime(A152597(n)). - Amiram Eldar, Nov 16 2023

Mathematica

r=0; p=3; L={}; While[Length@L < 20, v = (p-1)/ MultiplicativeOrder[2, p]; If[v > r, r = v; AppendTo[L, p]]; p = NextPrime@ p]; L (* Giovanni Resta, Aug 31 2015 *)

Prog

(PARI) r=0; forprime(p=3, 1e9, t=(p-1)/znorder(Mod(2, p)); if(t>r, r=t; print1(p", ")))

Crossrefs

Cf. A000668, A001917, A014664, A152597, A152598.

Sequence in context: A091383 A166501 A261862 * A244114 A072881 A257924

Adjacent sequences: A226213 A226214 A226215 * A226217 A226218 A226219

Keyword

nonn

Author

Charles R Greathouse IV, May 31 2013

Status

approved