cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A344661 Integers k such that k^2 is the sum of two Fibonacci numbers.

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%I A344661 #28 Feb 17 2023 07:40:01
%S A344661 0,1,2,3,4,6,12,40,3864
%N A344661 Integers k such that k^2 is the sum of two Fibonacci numbers.
%C A344661 Is this sequence finite?
%C A344661 No other terms below 10^20899.
%H A344661 F. Luca and V. Patel, <a href="https://doi.org/10.1016/j.jnt.2018.02.003">On perfect powers that are sums of two Fibonacci numbers</a>, J. Number Theory, 189:90-96, 2018.
%e A344661 These square sums of Fibonacci numbers correspond to:
%e A344661      0^2 = F(0)  + F(0);
%e A344661      1^2 = F(1)  + F(0)  = F(2) + F(0);
%e A344661      2^2 = F(4)  + F(1)  = F(4) + F(2) = F(3) + F(3);
%e A344661      3^2 = F(6)  + F(1)  = F(6) + F(2);
%e A344661      4^2 = F(7)  + F(4)  = F(6) + F(6);
%e A344661      6^2 = F(9)  + F(3);
%e A344661     12^2 = F(11) + F(10) = F(12) + F(0);
%e A344661     40^2 = F(17) + F(4);
%e A344661   3864^2 = F(36) + F(12).
%Y A344661 Cf. A000045, A007298, A084176, A111378, A219114.
%K A344661 nonn,hard,more
%O A344661 1,3
%A A344661 _Lamine Ngom_, May 26 2021