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

1,1

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.

Links

Table of n, a(n) for n=1..13.

Example

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

Prog

(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)

Crossrefs

Sequence in context: A180686 A308822 A289190 * A282466 A060724 A064949

Adjacent sequences: A145488 A145489 A145490 * A145492 A145493 A145494

Keyword

base,nonn,more

Author

Sébastien Dumortier and Bastien Lapeyre, Oct 11 2008

Status

approved