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A276501 Smallest number k such that k! has at least n terms in its Zeckendorf representation.

%I A276501 #30 Jun 15 2018 02:51:25
%S A276501 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 A276501 20,20,21,21,21,22,22,26,26,26,26,26,26,26,28,28,31,31,32,32,32,34,34,
%U A276501 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 A276501 Smallest number k such that k! has at least n terms in its Zeckendorf representation.
%C A276501 Least k >= 0 such that A007895(A000142(k)) >= n.
%C A276501 Corresponding factorial numbers are 1, 6, 120, 120, 5040, 40320, ...
%H A276501 Chai Wah Wu, <a href="/A276501/b276501.txt">Table of n, a(n) for n = 1..10038</a>
%e A276501 a(4) = 5 because Fibonacci(3) + Fibonacci(6) + Fibonacci(8) + Fibonacci(11) = 2 + 8 + 21 + 89 = 120 = 5!.
%o A276501 (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 A276501 a(n) = {my(k = 0); while(a007895(k!) < n, k++); k; }
%Y A276501 Cf. A000045, A000142, A007895, A182577.
%K A276501 nonn
%O A276501 1,2
%A A276501 _Altug Alkan_, Sep 06 2016