A328614 Number of 1-digits in primorial base expansion of n.

0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 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 two of these digits are "1"'s, 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. A049345, A056169, A267263, A276086, A328615, A328616.

Cf. A143293 (positions of records after initial zero).

Cf. also A257511.

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

A328614(n) = { my(s=0, p=2); while(n, s += (1==(n%p)); n = n\p; p = nextprime(1+p)); (s); };

Formula

a(n) = A056169(A276086(n)).

a(n) = A267263(n) - A328615(n).

For n >= 1, a(A143293(n-1)) = n. [This is the first occurrence of each n]