A215824 Odd numbers k such that the Fibonacci number F(k) can be written in the form a^2 + 3*b^2.

1, 7, 17, 23, 25, 47, 49, 71, 73, 79, 89, 119, 137, 151, 167, 191, 193, 199, 257, 271, 353, 359, 391, 409, 431, 433, 449, 569, 601, 719, 751, 799, 809, 823, 833, 857, 881, 887, 929, 953

Offset

1,2

Comments

These Fibonacci numbers F(k) have no prime factor congruent to 2 (mod 3) to an odd power.

Links

Table of n, a(n) for n=1..40.

Blair Kelly, Fibonacci and Lucas factorizations

Prog

(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", ")))

Crossrefs

Cf. A000045, A215822, A215823, A215825.

Sequence in context: A070416 A087168 A247560 * A239210 A191087 A032454

Adjacent sequences: A215821 A215822 A215823 * A215825 A215826 A215827

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

18 more terms from V. Raman, Aug 28 2012

Status

approved