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
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
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