A109631 Smallest number m such that n divides (10's complement factorial of m).

1, 2, 1, 2, 5, 2, 3, 2, 1, 5, 12, 2, 22, 3, 5, 4, 15, 2, 24, 5, 3, 12, 31, 2, 10, 22, 4, 3, 13, 5, 38, 6, 12, 15, 5, 2, 26, 24, 22, 5, 18, 3, 14, 12, 5, 31, 53, 4, 16, 10, 15, 22, 47, 4, 12, 3, 24, 13, 41, 5, 39, 38, 3, 6, 22, 12, 33, 15, 31, 5, 29, 2, 27, 26

Offset: 1

Author

Jason Earls, Aug 03 2005

Keywords

• nonn
• base

Comments

Are 374 and 2057 the only n such that a(n) = a(n+1)?

Examples

			a(7)=3 because 7 divides (10-3)*(10-2)*(10-1) and 7 does not divide (10's complement factorial of k) for k < 3.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002034, A109640, A110396.

Programs

PARI

g(p, e) = my(t=0); for(i=logint(p, 10), oo, forstep(j=10^i+(9*10^i)%p, 10^(i+1)-1, p, if(e<=t+=valuation(10^(i+1)-j, p), return(j))));
a(n) = my(m=1); foreach(factor(n)~, f, m=max(m, g(f[1], f[2]))); m; \\ Jinyuan Wang, Aug 09 2025