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
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
Programs
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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