A270059 Number of distinct digits needed to write n in all bases >= 2.

1, 1, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34

Offset

0,3

Links

Table of n, a(n) for n=0..66.

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

For n >= 3, a(n) = floor((n + 3)/2).

G.f.: 1 + (x*(1 + 2*x - x^2 - 2*x^3 + x^4))/((-1 + x)^2*(1 + x)). - Michael De Vlieger, Mar 09 2016

Example

4 written in all bases 2,3,4,5,6,7,... is 100,11,10,4,4,4,... and the distinct digits needed are 0, 1 and 4, so a(4) = 3.

Mathematica

Table[Length[Union@ Flatten@ Map[IntegerDigits[n, #] &, Range[2, n + 1]] /. {} -> {0}], {n, 0, 120}] (* or *)
Table[Length[Union@ Flatten@ Map[IntegerDigits[n, #] &, Range[2, n + 1]] /. {} -> {0}], {n, 0, 2}]~Join~Table[Floor[(n + 3)/2], {n, 3, 120}] (* or *)
CoefficientList[Series[1 + (x (1 + 2 x - x^2 - 2 x^3 + x^4))/((-1 + x)^2 (1 + x)), {x, 0, 120}], x] (* Michael De Vlieger, Mar 09 2016 *)

Prog

(PARI) a(n) = {if (n <= 1, 1, v = []; for (b=2, n+1, v = vecsort(concat(v, digits(n, b)), , 8)); #v; ); } \\ Michel Marcus, Mar 09 2016

Crossrefs

Cf. A008619, A266977.

Sequence in context: A361469 A073750 A378658 * A120204 A177018 A156349

Adjacent sequences: A270056 A270057 A270058 * A270060 A270061 A270062

Keyword

nonn,base

Author

Gionata Neri, Mar 09 2016

Status

approved