A215906 Even numbers n such that the Lucas number L(n) is the sum of two squares.

0, 6, 30, 78, 150, 390, 606, 750, 1434

Offset: 1

Author

V. Raman, Aug 26 2012

Keywords

• nonn
• more

Comments

These Lucas numbers L(n) have no prime factor congruent to 3 mod 4 to an odd power.

1758, 1950, 3030 are terms. - Chai Wah Wu, Jul 23 2020

Links

• Blair Kelly, Fibonacci and Lucas factorizations
• Eric W. Weisstein, Sum of squares function

Crossrefs

Cf. A000032, A124130, A215809, A215907.

Programs

Mathematica

Select[Range[0, 200, 2], Length[FindInstance[x^2 + 1*y^2 == LucasL[#], {x, y}, Integers]] > 0 &] (* G. C. Greubel, Apr 14 2017 *)

PARI

for(i=2, 500, a=factorint(fibonacci(i-1)+fibonacci(i+1))~; has=0; for(j=1, #a, if(a[1, j]%4==3&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==0, print(i", ")))

Extensions

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

a(6)-a(8) from V. Raman, Aug 28 2012

a(9) from Chai Wah Wu, Jul 23 2020