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

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

0,8

Comments

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 ...

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

a[n_Integer]:=Module[{f, i}, If[n<0, 0, f=Fibonacci[n]; i=Floor[Sqrt[f]]; Min[f-i^2, (i+1)^2-f]]]
Table[a[n], {n, 0, 70}] (* Vincenzo Librandi, Jan 20 2026 *)

Prog

(SageMath)
def a(n):
    f = fibonacci(n)
    return min((floor(sqrt(f))+1)^2 - f, f - floor(sqrt(f))^2)
(PARI) {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 */
(Magma) a := function(n) local f, i; if n lt 0 then return 0; end if; f := Fibonacci(n); i := Floor(Sqrt(f)); return Minimum(f - i^2, (i + 1)^2 - f); end function; [ a(n) : n in [0..70] ]; // Vincenzo Librandi, Jan 20 2026

Crossrefs

Sequence in context: A372862 A143052 A297104 * A269868 A344968 A324340

Adjacent sequences: A243253 A243254 A243255 * A243257 A243258 A243259

Keyword

nonn

Author

Ralf Stephan, Jun 02 2014

Status

approved