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%I #31 Jan 03 2022 20:32:58
%S 2,3,11,13,23,47,59,61,71,83,107,109,131,157,167,179,191,193,227,251,
%T 337,359,383,397,431,433,587,601,647,877,911,947,1091,1093
%N Prime numbers p such that the Fibonacci number F(p) can be written in the form a^2 + 2*b^2.
%C These Fibonacci numbers F(p) have no prime factor congruent to 5 or 7 (mod 8) 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]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))
%Y Cf. A000040, A000045, A030426, A215818, A215820, A215821.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 12 more terms from _V. Raman_, Aug 28 2012