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%I #32 Jul 23 2020 02:40:12
%S 0,6,30,78,150,390,606,750,1434
%N Even numbers n such that the Lucas number L(n) is the sum of two squares.
%C These Lucas numbers L(n) have no prime factor congruent to 3 mod 4 to an odd power.
%C 1758, 1950, 3030 are terms. - _Chai Wah Wu_, Jul 23 2020
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Fibonacci and Lucas factorizations</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/SumofSquaresFunction.html">Sum of squares function</a>
%t Select[Range[0, 200, 2], Length[FindInstance[x^2 + 1*y^2 == LucasL[#], {x, y}, Integers]] > 0 &] (* _G. C. Greubel_, Apr 14 2017 *)
%o (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", ")))
%Y Cf. A000032, A124130, A215809, A215907.
%K nonn,more
%O 1,2
%A _V. Raman_, Aug 26 2012
%E 0 added by _T. D. Noe_, Aug 27 2012
%E a(6)-a(8) from _V. Raman_, Aug 28 2012
%E a(9) from _Chai Wah Wu_, Jul 23 2020
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