A199575 a(n) = floor(Fibonacci(n)^(1/4)).

0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 21, 23, 26, 30, 34, 38, 43, 48, 55, 62, 70, 79, 89, 100, 113, 127, 144, 162, 183, 207, 233, 263, 296, 334, 377, 426, 480, 541, 611, 689, 777, 876, 989, 1115, 1258, 1418, 1600, 1804, 2035, 2295, 2589, 2920, 3293, 3714, 4189, 4725, 5329, 6010, 6778

Offset: 0

Author

N. J. A. Sloane, Nov 09 2011

Keywords

• nonn

Comments

The Ferraro problem asks for a proof that, for n>=9, floor(F(n)^(1/4)) = floor(F(n-4)^(1/4)+F(n-8)^(1/4)). As of November 2005 this problem remained unsolved.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• P. J. Ferraro, Problem B-886, Fibonacci Q., 37 (No. 4, Nov. 1999); 43 (No. 4, Nov. 2005), p. 372.
• Raphael Schumacher, Solution to Problem B-886, Fibonacci Q., 58 (No. 4, Nov. 2020) pp. 368-370.

Crossrefs

Cf. A061287.

Programs

Magma

[Floor(Fibonacci(n)^(1/4)): n in [0..80]]; // Vincenzo Librandi, Aug 28 2016

Mathematica

Table[Floor[Fibonacci[n]^(1/4)], {n, 0, 80}] (* Vincenzo Librandi, Aug 28 2016 *)

PARI

a(n) = sqrtnint(fibonacci(n), 4); \\ Michel Marcus, Aug 28 2016