A373598 a(n) = 1 if n and A327860(n) are both multiples of 3, where A327860 is the arithmetic derivative of the primorial base exp-function.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Comments

Apparently the asymptotic mean is 1/18, although this is not a characteristic function for the multiples of 18.

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

Formula

a(n) = [A351083(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

a(n) = A079978(n) * A369653(n).

a(n) = A373143(A276086(n)).

If a(x) = a(y) = A329041(x,y) = 1, then a(x+y) = 1 also. See explanation in the comments of A373599.

Prog

(PARI)
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A373598(n) = (!(n%3) && !(A327860(n)%3));

Crossrefs

Characteristic function of A373599.

Cf. A079978, A276086, A327860, A329041, A351083, A369653, A373143.

Sequence in context: A000007 A240351 A358008 * A249832 A014041 A373258

Adjacent sequences: A373595 A373596 A373597 * A373599 A373600 A373601

Keyword

nonn

Author

Antti Karttunen, Jun 18 2024

Status

approved