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A353087
Smallest integer k such that k! contains at least n copies of each decimal digit.
1
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
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
Sequence in context: A146595 A230123 A049851 * A223606 A120147 A166499
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Apr 22 2022
STATUS
approved