A373256 a(n) = 1 if A003415(n) == -1 (mod 3), otherwise 0, where A003415 is the arithmetic derivative.

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

Offset

0

Comments

Question: Do the asymptotic means of this sequence, A373254 and A359430 all converge to 1/3, or do they differ or diverge?

Links

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

Index entries for characteristic functions

Formula

a(n) = [A373253(n) == -1], where [ ] is the Iverson bracket.

a(n) = 1 - (A359430(n)+A373254(n)).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373256(n) = (2==(A003415(n)%3));

Crossrefs

Characteristic function of A373257.

Cf. A003415, A359430, A373253, A373254.

Sequence in context: A358842 A358758 A185708 * A286996 A044937 A025459

Adjacent sequences: A373253 A373254 A373255 * A373257 A373258 A373259

Keyword

nonn

Author

Antti Karttunen, Jun 01 2024

Status

approved