A220136 Number of ways that a number n can be written as ddd...d where d is a digit in base b with 1 < b < n-1.

0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 2, 0, 2, 2, 2, 1, 1, 1, 3, 0, 1, 1, 4, 0, 3, 1, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 2, 2, 1, 0, 5, 0, 2, 4, 2, 1, 3, 0, 2, 1, 3, 0, 4, 1, 1, 2, 2, 1, 3, 0, 5, 1, 1, 0, 5, 2, 2, 1

Offset: 1

Author

T. D. Noe, Dec 26 2012

Keywords

• nonn

Comments

When a(n) > 0, n is called Brazilian (A125134). The first number having exactly k representations is A284758(k) for k >= 0 or A066460(k+1) for k > 0. - Bernard Schott, Apr 08 2017

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066460, A125134, A284758.

Programs

Mathematica

brazBases[n_] := Select[Range[2, n - 2], Length[Union[IntegerDigits[n, #]]] == 1 &]; Table[Length[brazBases[n]], {n, 100}]

PARI

a(n) = sum(i=2, n-2, #vecsort(digits(n,i), , 8)==1) \\ David A. Corneth, Apr 08 2017