A239437 Least number that is pandigital in some base >= n but not pandigital in bases 3 through n-1.

11, 78, 698, 12280, 179685, 5518135, 1037845296, 1037845296, 46935813565, 2860727439460, 285947759601954, 1018897102759406, 672654273047783383

Offset: 3

Author

Charles R Greathouse IV, Mar 18 2014

Keywords

• nonn
• base
• hard

Comments

Gives an upper bound on the testing needed to check membership in A239348.

Links

• Charles R Greathouse IV, GP script for computing terms

Crossrefs

Subsequence of A154314. Cf. A239348.

Programs

PARI

See Greathouse link.

Python

from itertools import permutations
from gmpy2 import digits
def A239437(n): # requires 3 <= n <= 62
    m = n
    while True:
        s = ''.join([digits(i,m) for i in range(m)])
        for d in permutations(s,m):
            if d[0] != '0':
                c = mpz(''.join(d),m)
                for b in range(3,n):
                    if len(set(digits(c,b))) == b:
                        break
                else:
                    return int(c)
        m += 1 # Chai Wah Wu, May 31 2015

Formula

Trivially a(n) >= A049363(n) > n^(n-1).

Extensions

a(15) from Giovanni Resta, Mar 19 2014