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%I #30 Jan 03 2022 21:10:28
%S 2,7,17,23,47,71,73,79,89,137,151,167,191,193,199,257,271,353,359,409,
%T 431,433,449,569,601,719,751,809,823,857,881,887,929,953
%N Prime numbers p such that the Fibonacci number F(p) can be written in the form a^2 + 3*b^2.
%C These Fibonacci numbers F(p) have no prime factor congruent to 2 (mod 3) to an odd power.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Fibonacci and Lucas factorizations</a>
%o (PARI) forprime(i=2, 500, a=factorint(fibonacci(i))~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))
%Y Cf. A000045, A215822, A215824, A215825.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 15 more terms from _V. Raman_, Aug 28 2012