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A229139 Smallest m such that Fibonacci(2n-1) = m^2 + k^2.

%I A229139 #13 Oct 11 2013 00:46:43
%S A229139 0,1,1,2,3,5,8,9,21,34,55,89,73,13,377,610,987,64,244,4155,4554,10946,
%T A229139 2191,28657,15857,74957,34022,29811,50481,134104,832040,162589,387938,
%U A229139 711703,1556305,6229800,4173137,4059539,1972951,51797450,4866315,165580141,46049477,202620393,348451533,181781990
%N A229139 Smallest m such that Fibonacci(2n-1) = m^2 + k^2.
%C A229139 Every odd-indexed Fibonacci number (A000045) is a sum of two squares (see A124134).
%C A229139 Which of the a(n) are not Fibonacci numbers?
%e A229139 A000045(2*6-1) = 89 = 5^2 + 8^2 so a(6)=5.
%e A229139 A000045(2*8-1) = 610 = 9^2 + 23^2 = 13^2 + 21^2, so a(8)=9.
%o A229139 (PARI) for(n=1, 10^6, t=fibonacci(2*n-1);s=sqrtint(t);forstep(i=s,1,-1,if(issquare(t-i*i),print1(sqrtint(t-i*i), ",");break)))
%o A229139 (Haskell)
%o A229139 a229139 1 = 0
%o A229139 a229139 n = head $
%o A229139    dropWhile (== 0) $ map (a037213 . (t -) . (^ 2)) [s, s - 1 ..]
%o A229139    where t = a000045 (2 * n - 1); s = a000196 t
%o A229139 -- _Reinhard Zumkeller_, Oct 11 2013
%Y A229139 Cf. A000045.
%Y A229139 Cf. A000196, A037213.
%K A229139 nonn
%O A229139 1,4
%A A229139 _Ralf Stephan_, Sep 15 2013