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

2,1

Comments

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

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.

Example

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
...

Prog

(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

Crossrefs

Sequence in context: A102031 A248865 A072386 * A350932 A369947 A198894

Adjacent sequences: A185119 A185120 A185121 * A185123 A185124 A185125

Keyword

nonn,base

Author

Per H. Lundow, Jan 16 2012

Status

approved