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

0, 1, 2, 3, 4, 6, 12, 40, 3864

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