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A216225

Distance between n^2 and next higher Fibonacci number.

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, 362, 311, 258, 203, 146, 87, 26, 573, 508, 441, 372, 301, 228, 153, 76, 984, 903, 820, 735, 648, 559, 468, 375, 280, 183, 84, 1580, 1477, 1372, 1265, 1156, 1045, 932

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..57.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS