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Smallest distance of the n-th Fibonacci number to the set of all square integers.
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%I #6 Jun 02 2014 09:48:56

%S 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,

%T 169,285,140,296,669,267,1449,343,1979,144,592,665,4223,699,5283,2872,

%U 19604,6477,21826,17999,16008,46080,31240,102696,8638,45526,95764

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

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

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

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

%o (Sage)

%o def a(n):

%o f = fibonacci(n)

%o return min((floor(sqrt(f))+1)^2 - f, f - floor(sqrt(f))^2)

%o (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 */

%K nonn

%O 0,8

%A _Ralf Stephan_, Jun 02 2014