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.

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

Offset: 1

Author

Sébastien Dumortier and Bastien Lapeyre, Oct 11 2008

Keywords

• base
• nonn
• more

Comments

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

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

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

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

Examples

			In base 5 : 11111[2] = 111[5].
In base 90 : 1111111111111[2] = 111[90].
		

Programs

Python

for b1 in range(2, 3):
   for b2 in range(b1+1, 10001):
       for m in range(2, 20):
           for n in range(2, m+1):
               if (1-b1**m)*(1-b2)==(1-b1)*(1-b2**n):
                   print("b1, b2=", b1, b2, " m, n=", m, n)