A276501 - OEIS

A276501

Smallest number k such that k! has at least n terms in its Zeckendorf representation.

0, 3, 5, 5, 7, 8, 9, 9, 9, 11, 11, 14, 14, 14, 14, 14, 15, 17, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 26, 26, 26, 26, 26, 26, 26, 28, 28, 31, 31, 32, 32, 32, 34, 34, 34, 34, 34, 34, 35, 35, 35, 36, 38, 38, 38, 38, 38, 38, 38, 41, 41, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Least k >= 0 such that A007895(A000142(k)) >= n.

Corresponding factorial numbers are 1, 6, 120, 120, 5040, 40320, ...

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10038

EXAMPLE

a(4) = 5 because Fibonacci(3) + Fibonacci(6) + Fibonacci(8) + Fibonacci(11) = 2 + 8 + 21 + 89 = 120 = 5!.

PROG

(PARI) a007895(n) = if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s);