A346120 a(n) is the smallest nonnegative number k such that the decimal expansion of k! contains the string n.

5, 0, 2, 8, 4, 7, 3, 6, 9, 11, 19, 22, 5, 15, 26, 25, 11, 14, 27, 29, 5, 19, 13, 18, 4, 23, 26, 13, 9, 14, 15, 32, 8, 24, 28, 17, 9, 18, 23, 11, 7, 27, 17, 15, 21, 19, 26, 12, 24, 23, 7, 19, 23, 32, 29, 17, 17, 18, 23, 25, 12, 26, 9, 26, 18, 30, 20, 15, 11, 27, 13

Offset: 0

Author

Ilya Gutkovskiy, Jul 05 2021

Keywords

• nonn
• base

Examples

			a(3) = 8 since 3 occurs in 8! = 40320, but not in 0!, 1!, 2!, ..., 7!.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Richard V. Andree, Experiments with Natural Numbers, in: LeRoy C. Dalton and Henry D. Snyder (eds.), Topics for Mathematics Clubs, National Council of Teachers of Mathematics, 1973, Excursion 4, p. 64.

Crossrefs

Cf. A000142, A030000, A038690, A082058.

Programs

Mathematica

a[n_] := (k = 0; While[! MatchQ[IntegerDigits[k!], {_, Sequence @@ IntegerDigits[n], _}], k++]; k); Table[a[n], {n, 0, 70}]

PARI

a(n) = my(k=0, s=Str(n)); while (#strsplit(Str(k!), s) < 2, k++); k; \\ Michel Marcus, Jul 05 2021

Python

def A346120(n):
    s, k, f = str(n), 0, 1
    while s not in str(f):
        k += 1
        f *= k
    return k # Chai Wah Wu, Jul 05 2021