A215823 Prime numbers p such that the Fibonacci number F(p) can be written in the form a^2 + 3*b^2.

2, 7, 17, 23, 47, 71, 73, 79, 89, 137, 151, 167, 191, 193, 199, 257, 271, 353, 359, 409, 431, 433, 449, 569, 601, 719, 751, 809, 823, 857, 881, 887, 929, 953

Offset

1,1

Comments

These Fibonacci numbers F(p) have no prime factor congruent to 2 (mod 3) 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]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))

Crossrefs

Cf. A000045, A215822, A215824, A215825.

Sequence in context: A049546 A049578 A162574 * A049542 A049582 A220273

Adjacent sequences: A215820 A215821 A215822 * A215824 A215825 A215826

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

15 more terms from V. Raman, Aug 28 2012

Status

approved