A215819 Prime numbers p such that the Fibonacci number F(p) can be written in the form a^2 + 2*b^2.

2, 3, 11, 13, 23, 47, 59, 61, 71, 83, 107, 109, 131, 157, 167, 179, 191, 193, 227, 251, 337, 359, 383, 397, 431, 433, 587, 601, 647, 877, 911, 947, 1091, 1093

Offset

1,1

Comments

These Fibonacci numbers F(p) have no prime factor congruent to 5 or 7 (mod 8) to an odd power.

Links

Table of n, a(n) for n=1..34.

Blair Kelly, Fibonacci and Lucas factorizations

Prog

(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", ")))

Crossrefs

Cf. A000040, A000045, A030426, A215818, A215820, A215821.

Sequence in context: A163498 A038874 A164624 * A040101 A045317 A215378

Adjacent sequences: A215816 A215817 A215818 * A215820 A215821 A215822

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

12 more terms from V. Raman, Aug 28 2012

Status

approved