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A145491 In these bases, there exist numbers written with only one distinct digit whose translation in binary is also written with the same lonely digit.

%I A145491 #12 Apr 08 2025 18:28:34
%S A145491 5,6,14,30,62,90,126,254,510,1022,2046,4094,8190
%N A145491 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 A145491 All terms are equal to 2^n-2, except 5 and 90.
%C A145491 In base 2^n-2, we need 2 digits when there are n digits in binary.
%C A145491 In base 5, we need 3 digits for 5 digits in binary.
%C A145491 In base 90, we need 3 digits for 13 digits in binary.
%e A145491 In base 5 : 11111[2] = 111[5].
%e A145491 In base 90 : 1111111111111[2] = 111[90].
%o A145491 (Python)
%o A145491 for b1 in range(2, 3):
%o A145491    for b2 in range(b1+1, 10001):
%o A145491        for m in range(2, 20):
%o A145491            for n in range(2, m+1):
%o A145491                if (1-b1**m)*(1-b2)==(1-b1)*(1-b2**n):
%o A145491                    print("b1, b2=", b1, b2, " m, n=", m, n)
%K A145491 base,nonn,more
%O A145491 1,1
%A A145491 _Sébastien Dumortier_ and Bastien Lapeyre, Oct 11 2008