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

Offset: 1

Author

Altug Alkan, Sep 06 2016

Keywords

• nonn

Comments

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

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

Examples

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

Links

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

Crossrefs

Cf. A000045, A000142, A007895, A182577.

Programs

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);
a(n) = {my(k = 0); while(a007895(k!) < n, k++); k; }