A325431 a(n) is the least number not 3*a(m) or 4*a(m) for any m < n.

1, 2, 5, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 25, 26, 29, 31, 32, 34, 35, 37, 38, 41, 43, 45, 46, 47, 49, 50, 53, 55, 58, 59, 60, 61, 62, 63, 65, 67, 70, 71, 73, 74, 77, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 94, 95, 97, 98, 99, 101

Offset: 1

Author

Clark Kimberling, May 01 2019

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A325417, A325432.

Programs

Mathematica

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/4}],
IntegerQ]]] &]], {150}]; a          (* A325431 *)
Complement[Range[Last[a]], a]       (* A325432 *)
(* Peter J. C. Moses, Apr 25 2019 *)
Select[Range[100], Equal @@ Mod[IntegerExponent[#, {3, 4}], 2] &] (* Amiram Eldar, Sep 20 2020 *)