A270832 Number of bases in which n is written using more than 1 digit, all of which are distinct.

0, 1, 1, 1, 2, 3, 4, 4, 5, 5, 8, 7, 9, 9, 11, 10, 12, 12, 16, 14, 16, 16, 18, 17, 19, 19, 22, 22, 24, 23, 25, 24, 27, 27, 30, 27, 30, 32, 34, 32, 35, 34, 36, 37, 38, 38, 41, 39, 42, 41, 45, 45, 48, 47, 48, 48, 49, 51, 53, 48, 53, 54, 55, 53, 57, 58, 60, 60, 63, 62

Offset: 1

Author

André Engels, Mar 23 2016

Keywords

• nonn
• base

Comments

n/2 - 1 <= a(n) < n.

a(n) is not always <= n - sqrt(n) + 1. Counterexample: for n = 1000000, a(n) = 999911 > 999001 = n - sqrt(n) + 1. - Lucas O. Wagner, Jul 27 2019

Examples

			a(5) = 2 because 5 equals 10 in base 5, 12 in base 3. In base 2 (101) and base 4 (11) there are repeated digits, in base > 5 it is only one digit long.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Table[Count[Function[b, AllTrue[DigitCount[n, b], # <= 1 &]] /@ Range[2, n], True], {n, 70}] (* Michael De Vlieger, Mar 24 2016, Version 10 *)

PARI

a(n) = sum(b=2, n, v = digits(n,b); (#v > 1) && (#v == #Set(v))); \\ Michel Marcus, Mar 24 2016