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

1,2

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

Table of n, a(n) for n=1..9.

Blair Kelly, Fibonacci and Lucas factorizations

Eric W. Weisstein, Sum of squares function

Mathematica

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

Prog

(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", ")))

Crossrefs

Cf. A000032, A124130, A215809, A215907.

Sequence in context: A163640 A199130 A152743 * A305163 A038039 A258903

Adjacent sequences: A215903 A215904 A215905 * A215907 A215908 A215909

Keyword

nonn,more

Author

V. Raman, Aug 26 2012

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

Status

approved