A185122 a(n) = minimum pandigital prime in base n.

2, 11, 283, 3319, 48761, 863231, 17119607, 393474749, 10123457689, 290522736467, 8989787252711, 304978405943587, 11177758345241723, 442074237951168419, 18528729602926047181, 830471669159330267737, 39482554816041508293677, 1990006276023222816118943, 105148064265927977839670339, 5857193485931947477684595711

Offset: 2

Author

Per H. Lundow, Jan 16 2012

Keywords

• nonn
• base

Comments

a(n) is the smallest prime whose base-n representation contains all digits (i.e., 0,1,...,n-1) at least once.

Examples

			The corresponding base-b representations are:
2  10
3  102
4  10123
5  101234
6  1013425
7  10223465
8  101234567
9  1012346785
10 10123457689
11 1022345689a7
12 101234568a79b
13 10123456789abc
14 10123456789cdab
15 10223456789adbce
...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..386 (terms 2..100 from Per H. Lundow)
• Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 3.

Programs

Python

from math import gcd
from itertools import count
from sympy import nextprime
from sympy.ntheory import digits
def A185122(n):
    m = n
    j = 0
    if n > 3:
        for j in range(1,n):
            if gcd((n*(n-1)>>1)+j,n-1) == 1:
                 break
    if j == 0:
        for i in range(2,n):
            m = n*m+i
    elif j == 1:
        for i in range(1,n):
            m = n*m+i
    else:
        for i in range(2,1+j):
            m = n*m+i
        for i in range(j,n):
            m = n*m+i
    m -= 1
    while True:
        if len(set(digits(m:=nextprime(m),n)[1:]))==n:
            return m # Chai Wah Wu, Mar 12 2024