#math trivia for #September20: #263 has no digits in common with its base-N representation for which N < 10?

— Burt Kaliski Jr. (@modulomathy) September 21, 2013

The base-N representations of 263 for N = 2, …, 9 are:

- 100000111 base 2
- 100202 base 3
- 10013 base 4
- 2023 base 5
- 1115 base 6
- 524 base 7
- 407 base 8
- 322 base 9

The representations that don’t include at least one of the digits in 263 are N = 2, 6 and 8. In addition, if we count unary representation (which is sometimes considered base-1), then the representation for N = 1 doesn’t include one of the digits either. (The unary representation of 263 consists of 263 1’s.)