A369036 a(n) = 1 if A327860(n) is of the form 4m+2, otherwise 0, where A327860 is the arithmetic derivative of the primorial base exp-function.

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

Offset

0

Comments

Asymptotic mean seems to be 1/8. See comments in A369034.

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) = [A353630(n) == 2], where [ ] is the Iverson bracket.

a(n) = A121262(n) - A369034(n).

a(n) = A353495(A276086(n)).

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); };
A369036(n) = (2==(A327860(n)%4));

Crossrefs

Characteristic function of A369037.

Cf. A121262, A276086, A327860, A353495, A353630, A369034.

Sequence in context: A011669 A023971 A185014 * A354948 A330551 A346618

Adjacent sequences: A369033 A369034 A369035 * A369037 A369038 A369039

Keyword

nonn

Author

Antti Karttunen, Jan 20 2024

Status

approved