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

Author

Ralf Stephan, Jun 02 2014

Keywords

• nonn

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 ...

Programs

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 */

Sage

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

Formula

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