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

%I A373261 #18 Jul 19 2024 08:45:58
%S A373261 2,9,10,12,14,16,22,26,34,38,45,46,50,54,58,60,62,63,70,72,74,80,82,
%T A373261 84,86,94,96,98,99,106,110,112,117,118,122,128,130,132,134,142,146,
%U A373261 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
%N A373261 Numbers k for which A276085(k) == +1 (mod 3), where A276085 is the primorial base log-function.
%C A373261 Numbers k such that the 2-adic valuation of k minus the 3-adic valuation of k is equal to +1 modulo 3.
%C A373261 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).
%C A373261 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
%H A373261 Antti Karttunen, <a href="/A373261/b373261.txt">Table of n, a(n) for n = 1..10000</a>
%F A373261 {k such that A007814(k)-A007949(k) == +1 (mod 3)}.
%o A373261 (PARI)
%o A373261 A373260(n) = (1==((valuation(n,2)-valuation(n,3))%3));
%o A373261 isA373261 = A373260;
%Y A373261 Cf. A007814, A007949, A276085, A373260 (characteristic function).
%Y A373261 Positions of +1's in A373153.
%Y A373261 The positive integers are partitioned between A339746, this sequence, and A373262.
%K A373261 nonn
%O A373261 1,1
%A A373261 _Antti Karttunen_, May 30 2024