%I #13 Aug 04 2016 22:37:06
%S 3,13,97,193,241,673,769,12289,786433,22253377,39714817,152371201,
%T 597688321,1107296257,3221225473,7348420609,11560943617,29796335617,
%U 74490839041,77309411329,206158430209,246423748609,448203325441,2422022479873,5469640851457,28114855919617
%N Prime factors of numbers of the form 4^(2^m) - 2^(2^m) + 1 with m >= 0.
%C Primes p other than 3 such that one third of the multiplicative order of 2 (mod p) is a power of 2.
%C Primes in A255772 (except 7), sorted.
%H Arkadiusz Wesolowski, <a href="/A275528/b275528.txt">Table of n, a(n) for n = 1..27</a>
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-98-00891-6">Factors of generalized Fermat numbers</a>, Math. Comp. 67 (1998), no. 221, pp. 441-446.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-05-01816-8">Table errata to “Factors of generalized Fermat numbers”</a>, Math. Comp. 74 (2005), no. 252, p. 2099.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02371-9">Table errata 2 to "Factors of generalized Fermat numbers"</a>, Math. Comp. 80 (2011), pp. 1865-1866.
%e 3 divides 2^2 - 2^1 + 1 = 3.
%e 13 divides 2^4 - 2^2 + 1 = 13.
%e 97 divides 2^16 - 2^8 + 1 = 65281.
%e 193 divides 2^32 - 2^16 + 1 = 4294901761.
%e 241 divides 2^8 - 2^4 + 1 = 241.
%e 673 divides 2^16 - 2^8 + 1 = 65281.
%e 769 divides 2^128 - 2^64 + 1 = 340282366920938463444927863358058659841.
%e 12289 divides 2^2048 - 2^1024 + 1.
%o (PARI) forprime(p=3, 10^15, o=znorder(Mod(2, p))/3; x=ispower(2*o); if(p==3||2^(x-1)==o, print1(p, ", ")));
%Y Cf. A220294, A255772.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Jul 31 2016