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%I #10 Nov 05 2021 09:55:23
%S 2,3,5,17,29,43,47,113,127,179,197,257,277,283,293,317,383,439,449,
%T 467,479,509,569,641,659,719,797,863,1013,1069,1289,1373,1399,1427,
%U 1439,1487,1579,1627,1657,1753,1823,1913,1933,1949,2063,2203,2207,2213,2273,2339,2351
%N Primes p such that the length of the (eventual) period of the sequence {2^(2^k) mod p: k >= 0} is odd.
%C Of these numbers only 3 and 5 are elite primes (A102742). (Aigner)
%C Every prime of the form A036259(n)*2^m + 1, with m, n >= 1, is in this sequence.
%H Alexander Aigner, <a href="https://doi.org/10.1007/BF01298923">Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind</a>, Monatsh. Math., Vol. 101 (1986), pp. 85-93; <a href="https://eudml.org/doc/178266">alternative link</a>.
%o (PARI) L=List([2]); forprime(p=3, 2351, z=znorder(Mod(2, p)); if(znorder(Mod(2, z/2^valuation(z, 2)))%2, listput(L, p))); Vec(L)
%Y Supersequence of A023394.
%Y Cf. A102742 (elite primes), A256607.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Sep 26 2021