cp's OEIS Frontend

A243912 Numbers n > 1 such that n^k never ends in 2 or more identical digits for any k.

%I A243912 #13 May 22 2025 10:21:38
%S A243912 3,5,6,7,9,15,16,18,21,23,24,25,26,27,29,32,35,36,41,43,45,46,47,49,
%T A243912 51,56,57,61,63,65,67,68,69,74,75,76,81,82,83,85,86,87,89,93,95,96,
%U A243912 101,103,105,106,107,109,115,116,118,121,123,124,125,126,127,129,132,135,136,141
%N A243912 Numbers n > 1 such that n^k never ends in 2 or more identical digits for any k.
%C A243912 If n = 5^k for some k > 0, then n is in this sequence.
%C A243912 If n is a repdigit, then n is not in this sequence.
%C A243912 For n > 1, n is in this sequence iff n == {1, 3, 5, 6, 7, 9, 15, 16, 18, 21, 23, 24, 25, 26, 27, 29, 32, 35, 36, 41, 43, 45, 46, 47, 49, 51, 56, 57, 61, 63, 65, 67, 68, 69, 74, 75, 76, 81, 82, 83, 85, 86, 87, 89, 93, 95, 96} mod 100
%e A243912 5^k ends in 25 for all k > 1. Thus it will never end in any number of identical digits, and 5 is a member of this sequence.
%o A243912 (Python)
%o A243912 def b(n,p):
%o A243912   lst = []
%o A243912   count = 0
%o A243912   lst1 = []
%o A243912   for i in range(1,5**(n+2)):
%o A243912     st = str(p**i)
%o A243912     if len(st) >= n:
%o A243912       if int(st[len(st)-n:len(st)]) not in lst:
%o A243912         lst.append(int(st[len(st)-n:len(st)]))
%o A243912         lst1.append(i)
%o A243912       else:
%o A243912         return len(lst)+min(lst1)
%o A243912 def a(p):
%o A243912   for i in range(1,b(2,p)+2):
%o A243912     st = str(p**i)
%o A243912     if int(st[len(st)-2:len(st)])%11==0:
%o A243912       return i
%o A243912 p = 2
%o A243912 while p < 200:
%o A243912   if not a(p):
%o A243912     print(p,end=', ')
%o A243912   p += 1
%K A243912 nonn,base
%O A243912 1,1
%A A243912 _Derek Orr_, Jun 14 2014