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

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

Cf. A000290, A000045.

Sequence in context: A143096 A280225 A153058 * A276645 A293282 A240926

Adjacent sequences: A216222 A216223 A216224 * A216226 A216227 A216228

Keyword

nonn

Author

Carmine Suriano, Mar 13 2013

Status

approved