A373261 Numbers k for which A276085(k) == +1 (mod 3), where A276085 is the primorial base log-function.

2, 9, 10, 12, 14, 16, 22, 26, 34, 38, 45, 46, 50, 54, 58, 60, 62, 63, 70, 72, 74, 80, 82, 84, 86, 94, 96, 98, 99, 106, 110, 112, 117, 118, 122, 128, 130, 132, 134, 142, 146, 153, 154, 156, 158, 166, 170, 171, 176, 178, 182, 190, 194, 202, 204, 206, 207, 208, 214, 218, 225, 226, 228, 230, 238, 242, 243, 250, 254, 261

Offset: 1

Author

Antti Karttunen, May 30 2024

Keywords

• nonn

Comments

Numbers k such that the 2-adic valuation of k minus the 3-adic valuation of k is equal to +1 modulo 3.

When terms are multiplied by 3, forms a subsequence of A339746 (its multiples of 3), and when multiplied by 2, forms a subsequence of A373262 (its even terms).

More widely stated, the sequence lists one part of a 3-part partition of the positive integers with a symmetric relationship between the parts (further explained in the 2021 comment in A339746). - Peter Munn, Jul 19 2024

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A007949, A276085, A373260 (characteristic function).

Positions of +1's in A373153.

The positive integers are partitioned between A339746, this sequence, and A373262.

Programs

PARI

A373260(n) = (1==((valuation(n,2)-valuation(n,3))%3));
isA373261 = A373260;

Formula

{k such that A007814(k)-A007949(k) == +1 (mod 3)}.