A288157 Number of bases b < n where the digits of n are not all different.

0, 0, 1, 2, 2, 2, 2, 3, 3, 4, 2, 4, 3, 4, 3, 5, 4, 5, 2, 5, 4, 5, 4, 6, 5, 6, 4, 5, 4, 6, 5, 7, 5, 6, 4, 8, 6, 5, 4, 7, 5, 7, 6, 6, 6, 7, 5, 8, 6, 8, 5, 6, 4, 6, 6, 7, 7, 6, 5, 11, 7, 7, 7, 10, 7, 7, 6, 7, 5, 7, 6, 11, 6, 8, 7, 7, 6, 9, 6, 9, 9, 7, 5, 10, 7, 6, 7, 9, 7, 10, 8, 10, 8, 7, 6, 10, 7, 10, 6

Offset

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(10)=4 because 10 equals 1010 base 2 (repeating both 0 and 1), 101 base 3 (repeating 1), 22 base 4 (repeating 2) and 11 base 9 (repeating 1), and 20, 14, 13, 12 in the other bases < 10, not repeating digits.

Mathematica

Table[n - 1 - Boole[n > 1] - Count[Range[2, n - 1], b_ /; UnsameQ @@ IntegerDigits[n, b]], {n, 99}] (* Michael De Vlieger, Jun 15 2017 *)

Prog

(PARI) a(n) = sum(b=2, n, d = digits(n, b); #d != #Set(d)); \\ Michel Marcus, Jun 13 2017
(PARI) a(n)=my(s=sqrtint(n)); sum(b=2, s, my(d=digits(n, b)); #Set(d)!=#d) + sum(k=1, n\(s+1), n%k==0 && n/k>s+1) \\ Charles R Greathouse IV, Jun 15 2017

Crossrefs

a(n) = n - 1 - A270832(n).

Sequence in context: A032229 A024366 A218123 * A333701 A140682 A049317

Adjacent sequences: A288154 A288155 A288156 * A288158 A288159 A288160

Keyword

base,nonn,easy

Author

André Engels, Jun 06 2017

Status

approved