A349678 Primes p such that the multiplicative order of 2 modulo k is odd, where k is the largest odd divisor of p - 1.

2, 3, 5, 17, 29, 47, 113, 179, 197, 257, 293, 317, 383, 449, 467, 479, 509, 569, 659, 719, 797, 863, 1289, 1373, 1427, 1439, 1487, 1823, 1913, 1949, 2063, 2207, 2213, 2273, 2339, 2417, 2447, 2579, 2633, 2879, 2909, 3023, 3119, 3137, 3167, 3347, 3359, 3449, 3557

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(p) local k;
  if not isprime(p) then return false fi;
  k:= (p-1)/2^padic:-ordp(p-1, 2);
  numtheory:-order(2, k)::odd
end proc:
select(filter, [2, seq(i, i=3..10000, 2)]); # Robert Israel, Feb 02 2025

Mathematica

Select[Range[3600], PrimeQ[#] && OddQ[MultiplicativeOrder[2, (# - 1)/2^IntegerExponent[# - 1, 2]]] &] (* Amiram Eldar, Nov 26 2021 *)

Prog

(PARI) isok(p) = isprime(p) && znorder(Mod(2, (p-1)/2^valuation(p-1, 2)))%2;

Crossrefs

Subsequence of A348062.

Cf. A036259.

Sequence in context: A214735 A216061 A348062 * A029972 A077498 A118958

Adjacent sequences: A349675 A349676 A349677 * A349679 A349680 A349681

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 24 2021

Status

approved