This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382751 #40 Jul 23 2025 16:07:46
%S A382751 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,
%T A382751 37,38,40,41,43,44,46,47,49,50,52,53,54,55,56,58,59,61,62,64,65,67,68,
%U A382751 70,71,73,74,76,77,79,80,82,83,85,86,88,89,91,92,94,95
%N A382751 Numbers k for which the 3-adic valuation A007949(k) == 0 (mod 3).
%C A382751 Positive integers k for which the number of trailing 0 digits, which written in ternary, is a multiple of 3.
%C A382751 "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}.
%C A382751 In other words, s(S) is determined by the fact that {s(S), S*s(S)} is a partition of the positive integers.
%C A382751 The asymptotic density of this sequence is 9/13. - _Amiram Eldar_, Jul 23 2025
%H A382751 Jan Snellman, <a href="/A382751/b382751.txt">Table of n, a(n) for n = 1..6923</a>
%H A382751 Jan Snellman, <a href="https://arxiv.org/abs/2504.02795">Greedy Regular Convolutions</a>, arXiv:2504.02795 [math.NT], 2025.
%e A382751 7 is a term since its 3-adic valuation is A007949(7) = 0 which is == 0 (mod 3).
%t A382751 Select[Range[100], Divisible[IntegerExponent[#, 3], 3] &] (* _Amiram Eldar_, May 13 2025 *)
%o A382751 (PARI) isok(k) = (valuation(k, 3) % 3) == 0; \\ _Michel Marcus_, Jun 03 2025
%Y A382751 Cf. A007949, A007417.
%K A382751 nonn,easy
%O A382751 1,2
%A A382751 _Jan Snellman_, May 12 2025