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

0,4

Links

Cade Brown, Table of n, a(n) for n = 0..10000

Index entries for sequences related to primorial base

Formula

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

Example

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

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 *)

Prog

(PARI) cnz(n) = my(d = digits(n)); sum(k=1, #d, d[k]!=0);
A049345(n, p=2) = if(n<p, n, A049345(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

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.

Sequence in context: A193929 A132881 A224702 * A060130 A328482 A371091

Adjacent sequences: A267260 A267261 A267262 * A267264 A267265 A267266

Keyword

nonn,base

Author

Cade Brown, Jan 12 2016

Status

approved