A216225 - OEIS

%I #10 Mar 13 2013 15:38:55

%S 0,0,1,4,5,9,19,6,25,8,44,23,0,64,37,8,121,88,53,16,210,169,126,81,34,

%T 362,311,258,203,146,87,26,573,508,441,372,301,228,153,76,984,903,820,

%U 735,648,559,468,375,280,183,84,1580,1477,1372,1265,1156,1045,932

%N Distance between n^2 and next higher Fibonacci number.

%F a(n) = fib(x) - n^2 if fib(x) => n^2 and fib(x-1) < n^2; a(n)=0 for n=1, 12.

%e a(6) = 19 since 6^2 + 19 = 55 = fib(10) while fib(9) = 34 < 36.

%t k = 0; Table[While[n^2 > Fibonacci[k], k++]; Fibonacci[k] - n^2, {n, 0, 100}] (* _T. D. Noe_, Mar 13 2013 *)

%Y Cf. A000290, A000045.

%K nonn

%O 0,4

%A _Carmine Suriano_, Mar 13 2013