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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
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
Sequence in context: A220826 A095938 A018460 * A018484 A018496 A018521
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.)