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

0,1

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000142, A030000, A038690, A082058.

Sequence in context: A198883 A261850 A077496 * A190913 A019106 A051566

Adjacent sequences: A346117 A346118 A346119 * A346121 A346122 A346123

Keyword

nonn,base

Author

Ilya Gutkovskiy, Jul 05 2021

Status

approved