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 A344661 Integers k such that k^2 is the sum of two Fibonacci numbers. 0
 0, 1, 2, 3, 4, 6, 12, 40, 3864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Is this sequence finite? No other terms below 10^20899. LINKS Table of n, a(n) for n=1..9. F. Luca and V. Patel, On perfect powers that are sums of two Fibonacci numbers, J. Number Theory, 189:90-96, 2018. EXAMPLE These square sums of Fibonacci numbers correspond to: 0^2 = F(0) + F(0); 1^2 = F(1) + F(0) = F(2) + F(0); 2^2 = F(4) + F(1) = F(4) + F(2) = F(3) + F(3); 3^2 = F(6) + F(1) = F(6) + F(2); 4^2 = F(7) + F(4) = F(6) + F(6); 6^2 = F(9) + F(3); 12^2 = F(11) + F(10) = F(12) + F(0); 40^2 = F(17) + F(4); 3864^2 = F(36) + F(12). CROSSREFS Cf. A000045, A007298, A084176, A111378, A219114. Sequence in context: A220826 A095938 A018460 * A018484 A018496 A018521 Adjacent sequences: A344658 A344659 A344660 * A344662 A344663 A344664 KEYWORD nonn,hard,more AUTHOR Lamine Ngom, May 26 2021 STATUS approved

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Last modified June 21 07:08 EDT 2024. Contains 373540 sequences. (Running on oeis4.)