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

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base.

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]

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A049345, A056169, A267263, A276086, A328615, A328616.

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

Cf. also A257511.

Sequence in context: A089614 A064875 A216657 * A257511 A039802 A126726

Adjacent sequences: A328611 A328612 A328613 * A328615 A328616 A328617

Keyword

nonn,base

Author

Antti Karttunen, Oct 22 2019

Status

approved