cp's OEIS Frontend

A356739 a(n) is the smallest k such that k! has at least n consecutive zeros immediately after the leading digit in base 10.

%I A356739 #17 Oct 02 2022 00:23:54
%S A356739 7,153,197,7399,24434,24434,9242360,238861211,238861211
%N A356739 a(n) is the smallest k such that k! has at least n consecutive zeros immediately after the leading digit in base 10.
%e A356739 a(1) = 7, because 7! = 5040 has one zero immediately after the leading digit, and there is no k<7 with that property.
%o A356739 (Python)
%o A356739 from itertools import count
%o A356739 t = 1
%o A356739 n = 1
%o A356739 for k in count(1):
%o A356739     t *= k
%o A356739     while str(t)[1:1+n] == '0'*n:
%o A356739         print(n,k)
%o A356739         n += 1
%Y A356739 Cf. A000142, A027869.
%K A356739 nonn,base,more
%O A356739 1,1
%A A356739 _Christian Perfect_, Aug 25 2022
%E A356739 a(5)-a(6) from _Amiram Eldar_, Aug 25 2022
%E A356739 a(7)-a(9) from _Jinyuan Wang_, Aug 25 2022