cp's OEIS Frontend

A325417 a(n) is the least number not 2*a(m) or 3*a(m)+1 for any m < n.

%I A325417 #23 Mar 18 2021 04:21:33
%S A325417 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 A325417 44,45,47,48,49,50,51,53,55,56,57,59,60,63,65,67,68,69,71,73,74,75,76,
%U A325417 77,79,80,81,83,84,85,87,89,91,92,93,95,99,101,103,104
%N A325417 a(n) is the least number not 2*a(m) or 3*a(m)+1 for any m < n.
%C A325417 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 A325417 Disallowed    Sequence(a)  Complement(c)  Differences(a)  Differences(c)
%C A325417 2x, 3x+1      A325417      A325418        A325444         A325445
%C A325417 3x, 2x+1      A325419      A325420        A325494         A325495
%C A325417 2x+1, 3x+1    A077477      A325422        A325496         A325497
%C A325417 2x, 3x        A036668      A325424        A325498         A325499
%C A325417 [3x/2], 2x    A325425      A325426        A325518         A325519
%C A325417 [3x/2], 2x+1  A325427      A325428        A325520         A325521
%C A325417 [3x/2], 3x    A325429      A325430        A325522         A325523
%C A325417 3x, 4x        A325431      A325432        A325525         A325526
%C A325417 2x, 3x-1      A325462      A325463        A325526         A325527
%C A325417 2x, 3x-2      A325464      A325465        A325528         A325529
%C A325417 2x-1, 3x-1    A325440      A325441        A325530         A325531
%C A325417 2x-1, 3x      A325442      A325443        A325532         A325533
%C A325417 2x+1, 3x+2    A325539      A325540        A325541         A325542
%H A325417 Clark Kimberling, <a href="/A325417/b325417.txt">Table of n, a(n) for n = 1..10000</a>
%e A325417 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 A325417 a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
%t A325417 Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
%t A325417 IntegerQ]]] &]], {150}]; a     (* A325417 *)
%t A325417 Complement[Range[Last[a]], a]  (* A325418 *)
%t A325417 (* _Peter J. C. Moses_, Apr 23 2019 *)
%Y A325417 Cf. A325418, A325444.
%K A325417 nonn,easy
%O A325417 1,2
%A A325417 _Clark Kimberling_, Apr 24 2019