A216223 -id:A216223 - cp's OEIS frontend

A190993 Square excess of Fibonacci numbers.

0, 0, 0, 1, 2, 1, 4, 4, 5, 9, 6, 8, 0, 8, 16, 34, 26, 76, 84, 85, 41, 130, 22, 96, 143, 496, 289, 169, 842, 140, 296, 669, 2684, 1449, 343, 4096, 7583, 592, 665, 11682, 699, 20452, 2872, 22037, 6477, 21826, 17999, 93009, 46080, 31240, 121681, 8638, 317523

Offset: 0

Vladimir Joseph Stephan Orlovsky, Jun 02 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A000045, A190992, A216223.

[Fibonacci(n) - Floor(Sqrt(Fibonacci(n)))^2: n in [0..100]]; // G. C. Greubel, Oct 26 2022

a:= n-> (f-> f-floor(sqrt(f))^2)((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=0..52);  # Alois P. Heinz, Oct 26 2022

A000045=Fibonacci[Range[0,100]]; Table[A000045[[n]]-Floor[Sqrt[A000045[[n]]]]^2,{n,Length[A000045]}]

a(n) = my(f=fibonacci(n)); f - sqrtint(f)^2; \\ Michel Marcus, Nov 11 2015

[fibonacci(n) - isqrt(fibonacci(n))^2 for n in range(101)] # G. C. Greubel, Oct 26 2022

a(0) prepended by Alois P. Heinz, Nov 11 2015

A243256 Smallest distance of the n-th Fibonacci number to the set of all square integers.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 3, 4, 2, 6, 8, 0, 8, 16, 15, 26, 3, 17, 44, 41, 79, 22, 96, 143, 51, 289, 169, 285, 140, 296, 669, 267, 1449, 343, 1979, 144, 592, 665, 4223, 699, 5283, 2872, 19604, 6477, 21826, 17999, 16008, 46080, 31240, 102696, 8638, 45526, 95764

Offset: 0

Ralf Stephan, Jun 02 2014

nonn

a(n) = 0 if and only if n = 0, 1, 2, 12.

The sorted unique members: 0, 1, 2, 3, 4, 6, 8, 15, 16, 17, 22, 26 ...

{a(n) = my(f, i); if( n<0, 0, i = sqrtint( f = fibonacci(n))); min(f - i^2, (i+1)^2 - f)}; /* Michael Somos, Jun 02 2014 */

def a(n):
    f = fibonacci(n)
    return min((floor(sqrt(f))+1)^2 - f, f - floor(sqrt(f))^2)

a(n) = min(A190993(n), A216223(n)).

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A190993 Square excess of Fibonacci numbers.

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A243256 Smallest distance of the n-th Fibonacci number to the set of all square integers.

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