%I
%S 5,7,11,13,17,19,23,31,43,53,61,67,79,89,101,127,139,167,179,191,199,
%T 211,223,227,269,313,317,347,389,431,433,457,503,593,601,613,619,673,
%U 701,739,797,827,839,907,967
%N Prime numbers n such that (2^n+1)/3 can be written in the form a^2+7*b^2.
%C These numbers of the form (2^n+1)/3 have no prime factors congruent to 3 (mod 7) or 5 (mod 7) or 6 (mod 7) to an odd power. Also the power of 2 is not 1.
%H Samuel S. Wagstaff, Jr. <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%t Select[Prime[Range[170]],FindInstance[a^2+7b^2==(2^#+1)/3,{a,b},Integers] != {}&] (* _Harvey P. Dale_, Sep 04 2020 *)
%K nonn
%O 1,1
%A _V. Raman_, Sep 08 2012
