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A216223 Distance from Fibonacci(n) to the next perfect square. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Difference between y^2 and fib(n), y being next integer square root of fib(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

Table of n, a(n) for n=0..51.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. 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

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Last modified May 25 01:35 EDT 2019. Contains 323534 sequences. (Running on oeis4.)