A373830 a(n) = 1 if the primorial base representation of n has alternating digit sum that is a multiple of 3, otherwise 0.

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

Offset

0

Comments

a(n) = 1 if the multiplicities of prime factors of A276086(n) that are even-indexed (A031215) and odd-indexed (A031368) are equal modulo 3, otherwise 0.

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) = [A373605(n) == 0 (mod 3)].

Prog

(PARI)
A373605(n) = { my(p=2, i=1, s=0); while(n, s += i*(n%p); n = n\p; p = nextprime(1+p); i = -i); (s); };
A373830(n) = !(A373605(n)%3);

Crossrefs

Characteristic function of A373831.

Cf. A031215, A031368, A276086, A373604 [= a(6*n)], A373605.

Cf. also A079978 (characteristic function for multiples of 3), which can be obtained via an analogous construction for base-2 representation (substitute A065359 for A373605).

Sequence in context: A326072 A304362 A368997 * A330682 A230135 A359836

Adjacent sequences: A373827 A373828 A373829 * A373831 A373832 A373833

Keyword

nonn,base,new

Author

Antti Karttunen, Jun 19 2024

Status

approved