A066628 a(n) = n - the largest Fibonacci number <= n.

0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Offset: 0

Author

Amarnath Murthy, Dec 25 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A087172.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[Fibonacci[k] <= n, k++ ]; Return[n - Fibonacci[k - 1]]]; Table[ f[n], {n, 0, 100} ]

PARI

a(n) = { my(k=0); while(fibonacci(k) <= n, k++); n-fibonacci(k-1) } \\ Harry J. Smith, Mar 14 2010

Formula

a(n) = n - A087172(n). - Michel Marcus, Feb 02 2016

Extensions

Corrected and extended by Robert G. Wilson v, Dec 28 2001