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a(n) is the least number not 3*a(m) or 4*a(m) for any m < n.
7

%I #10 Sep 20 2020 12:12:44

%S 1,2,5,7,9,10,11,12,13,14,16,17,18,19,22,23,24,25,26,29,31,32,34,35,

%T 37,38,41,43,45,46,47,49,50,53,55,58,59,60,61,62,63,65,67,70,71,73,74,

%U 77,79,80,81,82,83,84,85,86,89,90,91,94,95,97,98,99,101

%N a(n) is the least number not 3*a(m) or 4*a(m) for any m < n.

%C Equivalently, numbers k whose exponent of the highest power of 3 dividing k and exponent of the highest power of 4 dividing k have the same parity. The asymptotic density of this sequence is 13/20. - _Amiram Eldar_, Sep 20 2020

%H Clark Kimberling, <a href="/A325431/b325431.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence necessarily starts with 1. The next 2 terms are determined as follows: because a(1) = 1, the numbers 3 and 4 are disallowed, so that a(2) = 2, whence the numbers 6 and 8 are disallowed, and a(3) = 5. See A325417 for a guide to related sequences.

%t a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,

%t Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/4}],

%t IntegerQ]]] &]], {150}]; a (* A325431 *)

%t Complement[Range[Last[a]], a] (* A325432 *)

%t (* _Peter J. C. Moses_, Apr 25 2019 *)

%t Select[Range[100], Equal @@ Mod[IntegerExponent[#, {3, 4}], 2] &] (* _Amiram Eldar_, Sep 20 2020 *)

%Y Cf. A325417, A325432.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 01 2019