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

1,2

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

Links

Jan Snellman, Table of n, a(n) for n = 1..6923

Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007949, A007417.

Sequence in context: A054386 A127450 A329843 * A292640 A059564 A329925

Adjacent sequences: A382748 A382749 A382750 * A382752 A382753 A382754

Keyword

nonn,easy

Author

Jan Snellman, May 12 2025

Status

approved