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

%I A349678 #11 Feb 03 2025 02:23:42
%S A349678 2,3,5,17,29,47,113,179,197,257,293,317,383,449,467,479,509,569,659,
%T A349678 719,797,863,1289,1373,1427,1439,1487,1823,1913,1949,2063,2207,2213,
%U A349678 2273,2339,2417,2447,2579,2633,2879,2909,3023,3119,3137,3167,3347,3359,3449,3557
%N A349678 Primes p such that the multiplicative order of 2 modulo k is odd, where k is the largest odd divisor of p - 1.
%H A349678 Robert Israel, <a href="/A349678/b349678.txt">Table of n, a(n) for n = 1..10000</a>
%p A349678 filter:= proc(p) local k;
%p A349678   if not isprime(p) then return false fi;
%p A349678   k:= (p-1)/2^padic:-ordp(p-1,2);
%p A349678   numtheory:-order(2,k)::odd
%p A349678 end proc:
%p A349678 select(filter, [2,seq(i,i=3..10000,2)]); # _Robert Israel_, Feb 02 2025
%t A349678 Select[Range[3600], PrimeQ[#] && OddQ[MultiplicativeOrder[2, (# - 1)/2^IntegerExponent[# - 1, 2]]] &] (* _Amiram Eldar_, Nov 26 2021 *)
%o A349678 (PARI) isok(p) = isprime(p) && znorder(Mod(2, (p-1)/2^valuation(p-1,2)))%2;
%Y A349678 Subsequence of A348062.
%Y A349678 Cf. A036259.
%K A349678 nonn
%O A349678 1,1
%A A349678 _Arkadiusz Wesolowski_, Nov 24 2021