A318725 a(n) is the smallest number k such that k! is pandigital in base n.

2, 8, 5, 11, 17, 14, 15, 23, 23, 24, 36, 30, 35, 46, 50, 43, 50, 40, 59, 62, 54, 69, 75, 70, 65, 79, 83, 68, 97, 99, 86, 89, 93, 97, 118, 94, 106, 126, 128, 116, 145, 127, 134, 151, 143, 124, 141, 124, 141, 170, 194, 169, 190, 183, 181, 180, 195, 195, 210, 163

Offset: 2

Author

Jon E. Schoenfield, Sep 02 2018

Keywords

• nonn
• base

Examples

			a(2) = 2! = 2_10 = 10_2;
a(3) = 8! = 40320_10 = 2001022100_3;
a(4) = 5! = 120_10 = 1320_4.
a(5) = 11! = 39916800_10 = 4020431420_5;
a(6) = 17! = 355687428096000_10 = 3300252314304000000_6.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..1348 (terms 2..1000 from Seiichi Manyama)

Crossrefs

Cf. A049363 (smallest pandigital number in base n), A185122 (smallest pandigital prime in base n), A260182 (smallest square that is pandigital in base n), A260117 (smallest triangular number that is pandigital in base n).

Programs

PARI

a(n) = {my(k=1); while (#Set(digits(k!, n)) != n, k++); k;} \\ Michel Marcus, Sep 02 2018

Python

from itertools import count
from sympy.ntheory import digits
def A318725(n):
    c, flag = 1, False
    for k in count(1):
        m = k
        if flag:
            a, b = divmod(m,n)
            while not b:
                m = a
                a, b = divmod(m,n)
        c *= m
        if len(set(digits(c,n)[1:]))==n:
            return k
        if not (flag or c%n):
            flag = True # Chai Wah Wu, Mar 13 2024