A267263 Number of nonzero digits in representation of n in primorial base.

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

Offset: 0

Author

Cade Brown, Jan 12 2016

Keywords

• nonn
• base

Examples

			a(3) = 2 because 3 written in primorial base is 11 with 2 nonzero digits.
		

Links

• Cade Brown, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to primorial base

Crossrefs

Cf. A001221, A002110, A049345, A235168, A276086.

Cf. A060735 (positions of ones).

A060130 is an analogous sequence for the factorial base, from which this differs for the first time at n=30, where a(30) = 1, while A060130(30) = 2.

Programs

Maple

a:= proc(n) local m, p, r; m, p, r:= n, 2, 0;
       while m>0 do r:= r+`if`(irem(m, p, 'm')>0, 1, 0);
                    p:= nextprime(p)
       od; r
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 15 2016

Mathematica

Table[Length[IntegerDigits[n, MixedRadix@ Prime@ Reverse@ Range@ PrimePi@ n] /. 0 -> Nothing], {n, 0, 120}] (* Michael De Vlieger, Jan 12 2016, Version 10.2 *)
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Prime@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Prime@ Range[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[Count[f@ n, d_ /; d > 0], {n, 0, 73}] (* Michael De Vlieger, Aug 29 2016 *)

PARI

cnz(n) = my(d = digits(n)); sum(k=1, #d, d[k]!=0);
A049345(n, p=2) = if(nA049345(n\p, nextprime(p+1))*10 + n%p)
a(n) = cnz(A049345(n)); \\ Michel Marcus, Jan 12 2016

PARI

a(n)=my(s); forprime(p=2,, if(n%p, s++, if(n==0, return(s))); n\=p) \\ Charles R Greathouse IV, Nov 17 2016

Formula

a(n) = A001221(A276086(n)). - Antti Karttunen, Aug 21 2016