A328620 Number of nonleading zeros in primorial base expansion of n, a(0) = 0 by convention.

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

Offset: 0

Author

Antti Karttunen, Oct 23 2019

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A001221, A002110, A049345, A079067, A276086, A328612, A328614, A328615, A328616.

Cf. A257510 for an analogous sequence.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r == 0, s++]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

PARI

A328620(n) = { my(s=0, p=2); while(n, s += (0==(n%p)); n = n\p; p = nextprime(1+p)); (s); };

Formula

a(n) = A001221(A328612(n)).

a(n) = A079067(A276086(n)).

a(A002110(n)) = n for all n >= 0.