%I #23 Mar 18 2021 04:21:33

%S 1,3,5,7,8,9,11,12,13,15,17,19,20,21,23,27,29,31,32,33,35,36,39,41,43,

%T 44,45,47,48,49,50,51,53,55,56,57,59,60,63,65,67,68,69,71,73,74,75,76,

%U 77,79,80,81,83,84,85,87,89,91,92,93,95,99,101,103,104

%N a(n) is the least number not 2*a(m) or 3*a(m)+1 for any m < n.

%C In column 1 of the following guide to related sequences, disallowed terms are indicated by the variable x representing a(m) for m < n.

%C Disallowed Sequence(a) Complement(c) Differences(a) Differences(c)

%C 2x, 3x+1 A325417 A325418 A325444 A325445

%C 3x, 2x+1 A325419 A325420 A325494 A325495

%C 2x+1, 3x+1 A077477 A325422 A325496 A325497

%C 2x, 3x A036668 A325424 A325498 A325499

%C [3x/2], 2x A325425 A325426 A325518 A325519

%C [3x/2], 2x+1 A325427 A325428 A325520 A325521

%C [3x/2], 3x A325429 A325430 A325522 A325523

%C 3x, 4x A325431 A325432 A325525 A325526

%C 2x, 3x-1 A325462 A325463 A325526 A325527

%C 2x, 3x-2 A325464 A325465 A325528 A325529

%C 2x-1, 3x-1 A325440 A325441 A325530 A325531

%C 2x-1, 3x A325442 A325443 A325532 A325533

%C 2x+1, 3x+2 A325539 A325540 A325541 A325542

%H Clark Kimberling, <a href="/A325417/b325417.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 2 and 4 are disallowed, so that a(2) = 3, whence the numbers 6 and 10 are disallowed, so that a(3) = 5.

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

%t Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],

%t IntegerQ]]] &]], {150}]; a (* A325417 *)

%t Complement[Range[Last[a]], a] (* A325418 *)

%t (* _Peter J. C. Moses_, Apr 23 2019 *)

%Y Cf. A325418, A325444.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 24 2019