A328615 Number of digits larger than 1 in primorial base expansion of n.

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

Offset: 0

Author

Antti Karttunen, Oct 22 2019

Keywords

• nonn
• base

Examples

			In primorial base (A049345), 87 is written as "2411" because 87 = 2*A002110(3) + 4*A002110(2) + 1*A002110(1) + 1*A002110(0) = 2*30 + 4*6 + 1*2 + 1*1. Only the digits 2 and 4 of these are larger than one, thus a(87) = 2.
		

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, A267263, A276086, A328114, A328572, A328614, A328616.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 1, s++]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

PARI

A328615(n) = { my(s=0, p=2); while(n, s += (1<(n%p)); n = n\p; p = nextprime(1+p)); (s); };

Formula

a(n) = A267263(n) - A328614(n).

a(n) = A001221(A328572(n)).