A373153 a(n) is -1, 0, or 1 such that a(n) == A276085(n) (mod 3), where A276085 is the primorial base log-function.

0, 1, -1, -1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, -1, 1, 0, -1, 0, -1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, -1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, -1, -1, 1, 0, 1, 0, 1, -1, -1, 0, 0, 0, 1, -1, 1, 0, 1, 0, 1, -1, 0, 0, -1, 0, -1, -1, 1, 0, 1, 0, 1, 1, -1, 0, 0, 0, 0, -1

Offset

1

Comments

Completely additive modulo 3.

a(n) is -1, 0, or 1 such that a(n) == A007814(n)-A007949(n) (mod 3). - Antti Karttunen, Jun 01 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial numbers

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A373153(n) = { my(f = factor(n), u); u=sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1))%3; if(2==u, -1, u); };
(PARI) A373153(n) = { my(u=(valuation(n, 2)-valuation(n, 3))%3); if(2==u, -1, u); }; \\ Antti Karttunen, Jun 01 2024

Crossrefs

Cf. A002110, A007814, A007949, A276085.

Cf. A339746 (positions of 0's), A373261 (of +1's), A373262 (of -1's).

Cf. also A332814, A332823, A373253.

Sequence in context: A138712 A029693 A200263 * A051067 A288858 A356313

Adjacent sequences: A373150 A373151 A373152 * A373154 A373155 A373156

Keyword

sign

Author

Antti Karttunen, May 27 2024

Status

approved