A353087 Smallest integer k such that k! contains at least n copies of each decimal digit.

23, 34, 40, 55, 59, 67, 75, 81, 90, 90, 97, 108, 118, 123, 131, 144, 147, 147, 147, 157, 157, 182, 186, 186, 186, 189, 203, 204, 206, 206, 209, 232, 232, 236, 236, 237, 237, 245, 257, 257, 265, 278, 282, 282, 282, 282, 282, 290, 307, 307, 318, 318, 318, 318, 341

Offset: 1

Author

Alois P. Heinz, Apr 22 2022

Keywords

• nonn
• base

Examples

			23! = 25852016738884976640000 is the smallest factorial containing at least one copy of each decimal digit. Thus a(1) = 23.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000142, A352040.

Programs

Maple

a:= proc(n) option remember; local k; for k from a(n-1)
      while min((p-> seq(coeff(p, x, j), j=0..9))(add(
            x^i, i=convert(k!, base, 10))))
				

Python

def A353087(n):
    k, m, r  = 1, 1, 10**(10*n-1)
    while m < r:
        k += 1
        m *= k
    s = str(m)
    while any(s.count(d) < n for d in '0123456789'):
        k += 1
        m *= k
        s = str(m)
    return k # Chai Wah Wu, Apr 22 2022