A382751 Numbers k for which the 3-adic valuation A007949(k) == 0 (mod 3).

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 54, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95

Offset: 1

Author

Jan Snellman, May 12 2025

Keywords

• nonn
• easy

Comments

Positive integers k for which the number of trailing 0 digits, which written in ternary, is a multiple of 3.

"Selective sifting" of the positive integers w.r.t. S={3,9}, where s(S) = {positive integers n: n cannot be written n = a*b with a in S, b in s(S), b < n}.

In other words, s(S) is determined by the fact that {s(S), S*s(S)} is a partition of the positive integers.

The asymptotic density of this sequence is 9/13. - Amiram Eldar, Jul 23 2025

Examples

			7 is a term since its 3-adic valuation is A007949(7) = 0 which is == 0 (mod 3).
		

Links

• Jan Snellman, Table of n, a(n) for n = 1..6923
• Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Crossrefs

Cf. A007949, A007417.

Programs

Mathematica

Select[Range[100], Divisible[IntegerExponent[#, 3], 3] &] (* Amiram Eldar, May 13 2025 *)

PARI

isok(k) = (valuation(k, 3) % 3) == 0; \\ Michel Marcus, Jun 03 2025