A373261 - OEIS

%I #18 Jul 19 2024 08:45:58

%S 2,9,10,12,14,16,22,26,34,38,45,46,50,54,58,60,62,63,70,72,74,80,82,

%T 84,86,94,96,98,99,106,110,112,117,118,122,128,130,132,134,142,146,

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

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

%C 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 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 Antti Karttunen, <a href="/A373261/b373261.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI)

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

%o isA373261 = A373260;

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

%Y Positions of +1's in A373153.

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

%K nonn

%O 1,1

%A _Antti Karttunen_, May 30 2024