A215820 Odd numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 2*b^2.

1, 3, 9, 11, 13, 23, 25, 33, 39, 47, 59, 61, 71, 83, 107, 109, 121, 131, 141, 157, 167, 179, 183, 191, 193, 227, 249, 251, 299, 321, 337, 359, 363, 383, 393, 397, 423, 431, 433, 471, 501, 517, 579, 587, 601, 647, 649, 877, 911, 913, 947, 1079, 1091, 1093

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..54.

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]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==1, print(i", ")))

Crossrefs

Cf. A000045, A215818, A215819, A215821.

Sequence in context: A287333 A174813 A116444 * A065136 A075720 A106373

Adjacent sequences: A215817 A215818 A215819 * A215821 A215822 A215823

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

1 added by T. D. Noe, Aug 27 2012

Added the number 25 and 21 more terms - V. Raman, Aug 28 2012

Status

approved