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 A215825 Even numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 3*b^2. 3
 2, 4, 8, 12, 34, 146, 706, 1138, 1714, 1762 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These Fibonacci numbers F(n) have no prime factor congruent to 2 mod 3 to an odd power. Note that F(12) = 144 = 2^4 * 3^2. - T. D. Noe, Aug 27 2012 LINKS Blair Kelly, Fibonacci and Lucas factorizations MATHEMATICA Select[Range[2, 200, 2], Length[FindInstance[x^2 + 3*y^2 == Fibonacci[#], {x, y}, Integers]] > 0 &] (* T. D. Noe, Aug 27 2012 *) PROG (PARI) for(i=2, 500, a=factorint(fibonacci(i))~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==0, print(i", "))) CROSSREFS Cf. A000045, A215822, A215823, A215824. Sequence in context: A007374 A105207 A202148 * A177268 A289085 A242924 Adjacent sequences:  A215822 A215823 A215824 * A215826 A215827 A215828 KEYWORD nonn AUTHOR V. Raman, Aug 23 2012 EXTENSIONS Edited by N. J. A. Sloane, Aug 23 2012 12 added by T. D. Noe, Aug 27 2012 Added 4 more terms - V. Raman, Aug 28 2012 STATUS approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)