login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Smallest number k such that k! has at least n terms in its Zeckendorf representation.
1

%I #30 Jun 15 2018 02:51:25

%S 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,

%T 20,20,21,21,21,22,22,26,26,26,26,26,26,26,28,28,31,31,32,32,32,34,34,

%U 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

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

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

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

%H Chai Wah Wu, <a href="/A276501/b276501.txt">Table of n, a(n) for n = 1..10038</a>

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

%o (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);

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

%Y Cf. A000045, A000142, A007895, A182577.

%K nonn

%O 1,2

%A _Altug Alkan_, Sep 06 2016