A215811 Prime numbers n such that the Lucas number L(n) can be written in the form a^2 + 3*b^2.

2, 3, 11, 17, 19, 41, 43, 67, 73, 83, 113, 139, 241, 281, 283, 313, 353, 379, 401, 443, 457, 569, 571, 577, 617, 857, 881, 1009, 1033, 1097

Offset

1,1

Comments

These Lucas numbers L(n) have no prime factor congruent to 2 mod 3 to an odd power.

Links

Table of n, a(n) for n=1..30.

Blair Kelly, Fibonacci and Lucas factorizations

Prog

(PARI) forprime(i=2, 500, a=factorint(fibonacci(i-1)+fibonacci(i+1))~; 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. A000032, A215810, A215815, A215816.

Sequence in context: A051082 A051080 A051098 * A051076 A192612 A014092

Adjacent sequences: A215808 A215809 A215810 * A215812 A215813 A215814

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

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

Added 12 more terms - V. Raman, Aug 28 2012

Status

approved