A215813 Prime numbers p such that the Lucas number L(p) can be written in the form a^2 + 2*b^2.

2, 3, 5, 13, 17, 29, 37, 41, 53, 61, 89, 97, 113, 137, 157, 197, 281, 313, 349, 353, 397, 433, 457, 461, 509, 541, 557, 593, 613, 617, 661, 673, 809, 829, 857, 877, 1061, 1097

Offset

1,1

Comments

These Lucas numbers L(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..38.

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

Crossrefs

Cf. A000032, A215812.

Sequence in context: A193761 A215355 A242752 * A235638 A227829 A231481

Adjacent sequences: A215810 A215811 A215812 * A215814 A215815 A215816

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

18 more terms from V. Raman, Aug 28 2012

Status

approved