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

Author

Charles R Greathouse IV, May 31 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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