(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a215939 Showing 1-1 of 1 %I A215939 #29 Feb 06 2013 11:07:48 %S A215939 2,5,11,29,41,89,131,179,331,359,401,421,431,449,509,569,571,601,631, %T A215939 659,691,911 %N A215939 Prime numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 5*b^2. %C A215939 A number n can be written in the form a^2+5*b^2 if and only if n is 0, or of the form 2^(2i) 5^j Prod_{p==1 or 9 mod 20} p^k Prod_{q==3 or 7 mod 20) q^(2m) or of the form 2^(2i+1) 5^j Prod_{p==1 or 9 mod 20} p^k Prod_{q==3 or 7 mod 20) q^(2m+1), for integers i,j,k,m, for primes p,q. %H A215939 Blair Kelly, Fibonacci and Lucas factorizations %o A215939 (PARI) forprime(i=2, 500, a=factorint(fibonacci(i))~; flag=0; flip=0; for(j=1, #a, if(((a[1, j]%20>10))&&a[2, j]%2==1, flag=1); if(((a[1, j]%20==2)||(a[1, j]%20==3)||(a[1, j]%20==7))&&a[2, j]%2==1, flip=flip+1)); if(flag==0&&flip%2==0, print(i", "))) %Y A215939 Cf. A000045, A215938, A124132. %Y A215939 Cf. A020669, A033205 (numbers and primes of the form x^2 + 5*y^2). %K A215939 nonn,more %O A215939 1,1 %A A215939 _V. Raman_, Aug 27 2012 %E A215939 Terms corrected by _V. Raman_, Sep 20 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE