A145491 - OEIS

%I #9 Feb 22 2015 14:58:13

%S 5,6,14,30,62,90,126,254,510,1022,2046,4094,8190

%N In these bases, there exist numbers written with only one distinct digit whose translation in binary is also written with the same lonely digit.

%C All terms are equal to 2^n-2, except 5 and 90.

%C In base 2^n-2, we need 2 digits when there are n digits in binary.

%C In base 5, we need 3 digits for 5 digits in binary.

%C In base 90, we need 3 digits for 13 digits in binary.

%e In base 5 : 11111[2] = 111[5].

%e In base 90 : 1111111111111[2] = 111[90].

%o (Python) from math import *

%o .for b1 in range(2,3):

%o ....for b2 in range(b1+1,10001):

%o ........for m in range(2,20):

%o ............for n in range(2,m+1):

%o ................if (1-b1**m)*(1-b2)==(1-b1)*(1-b2**n):

%o ....................print "b1,b2=",b1,b2," m,n=",m,n

%K base,nonn,more

%O 1,1

%A _Sébastien Dumortier_ and Bastien Lapeyre, Oct 11 2008