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

%I A185122 #28 Apr 04 2024 10:13:49
%S A185122 2,11,283,3319,48761,863231,17119607,393474749,10123457689,
%T A185122 290522736467,8989787252711,304978405943587,11177758345241723,
%U A185122 442074237951168419,18528729602926047181,830471669159330267737,39482554816041508293677,1990006276023222816118943,105148064265927977839670339,5857193485931947477684595711
%N A185122 a(n) = minimum pandigital prime in base n.
%C A185122 a(n) is the smallest prime whose base-n representation contains all digits (i.e., 0,1,...,n-1) at least once.
%H A185122 Chai Wah Wu, <a href="/A185122/b185122.txt">Table of n, a(n) for n = 2..386</a> (terms 2..100 from Per H. Lundow)
%H A185122 Chai Wah Wu, <a href="https://arxiv.org/abs/2403.20304">Pandigital and penholodigital numbers</a>, arXiv:2403.20304 [math.GM], 2024. See p. 3.
%e A185122 The corresponding base-b representations are:
%e A185122 2  10
%e A185122 3  102
%e A185122 4  10123
%e A185122 5  101234
%e A185122 6  1013425
%e A185122 7  10223465
%e A185122 8  101234567
%e A185122 9  1012346785
%e A185122 10 10123457689
%e A185122 11 1022345689a7
%e A185122 12 101234568a79b
%e A185122 13 10123456789abc
%e A185122 14 10123456789cdab
%e A185122 15 10223456789adbce
%e A185122 ...
%o A185122 (Python)
%o A185122 from math import gcd
%o A185122 from itertools import count
%o A185122 from sympy import nextprime
%o A185122 from sympy.ntheory import digits
%o A185122 def A185122(n):
%o A185122     m = n
%o A185122     j = 0
%o A185122     if n > 3:
%o A185122         for j in range(1,n):
%o A185122             if gcd((n*(n-1)>>1)+j,n-1) == 1:
%o A185122                  break
%o A185122     if j == 0:
%o A185122         for i in range(2,n):
%o A185122             m = n*m+i
%o A185122     elif j == 1:
%o A185122         for i in range(1,n):
%o A185122             m = n*m+i
%o A185122     else:
%o A185122         for i in range(2,1+j):
%o A185122             m = n*m+i
%o A185122         for i in range(j,n):
%o A185122             m = n*m+i
%o A185122     m -= 1
%o A185122     while True:
%o A185122         if len(set(digits(m:=nextprime(m),n)[1:]))==n:
%o A185122             return m # _Chai Wah Wu_, Mar 12 2024
%K A185122 nonn,base
%O A185122 2,1
%A A185122 _Per H. Lundow_, Jan 16 2012