%I #27 Jan 03 2022 21:10:39

%S 1,7,17,23,25,47,49,71,73,79,89,119,137,151,167,191,193,199,257,271,

%T 353,359,391,409,431,433,449,569,601,719,751,799,809,823,833,857,881,

%U 887,929,953

%N Odd numbers k such that the Fibonacci number F(k) can be written in the form a^2 + 3*b^2.

%C These Fibonacci numbers F(k) 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) for(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&&i%2==1, print(i", ")))

%Y Cf. A000045, A215822, A215823, A215825.

%K nonn

%O 1,2

%A _V. Raman_, Aug 23 2012

%E 18 more terms from _V. Raman_, Aug 28 2012