A216223 Distance from Fibonacci(n) to the next perfect square.

0, 0, 0, 2, 1, 4, 1, 3, 4, 2, 9, 11, 0, 23, 23, 15, 37, 3, 17, 44, 124, 79, 245, 243, 288, 51, 408, 718, 285, 1295, 1529, 1652, 267, 2306, 4434, 1979, 144, 9239, 11840, 4223, 19534, 5283, 29865, 19604, 46492, 45551, 67706, 16008, 92593, 145155, 102696, 276775

Offset

0,4

Comments

Difference between y^2 and Fibonacci(n), y being next integer square root of Fibonacci(n). a(n)=0 only for n = 0, 1, 2, 12.

a(n) is a square for n = 0, 1, 2, 4, 5, 6, 8, 10, 12, 36.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Formula

a(n) = floor(sqrt(Fibonacci(n))+1)^2-Fibonacci(n) if n<>1, 2, 12; else a(n)=0.

Example

a(5) = 4 since Fibonacci(5)=5 that differs 4 to next square that is 9.

Maple

a:= n-> (f-> ceil(sqrt(f))^2-f)((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=0..51);  # Alois P. Heinz, Oct 26 2022

Mathematica

Table[k = Ceiling[Sqrt[Fibonacci[n]]]; k^2 - Fibonacci[n], {n, 0, 60}] (* T. D. Noe, Mar 13 2013 *)

Crossrefs

Cf. A000045, A190993.

Sequence in context: A317837 A296074 A239451 * A078072 A306944 A049776

Adjacent sequences: A216220 A216221 A216222 * A216224 A216225 A216226

Keyword

nonn

Author

Carmine Suriano, Mar 13 2013

Status

approved