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

1,1

Links

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

Example

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

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))))<n do od; k
    end: a(0):=0:
seq(a(n), n=1..100);

Prog

(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

Crossrefs

Cf. A000142, A352040.

Sequence in context: A146595 A230123 A049851 * A223606 A120147 A166499

Adjacent sequences: A353084 A353085 A353086 * A353088 A353089 A353090

Keyword

nonn,base

Author

Alois P. Heinz, Apr 22 2022

Status

approved