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A258046 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

%I A258046 #8 Jun 05 2015 13:00:49
%S A258046 1,2,4,3,6,12,5,10,7,14,8,16,11,9,18,36,13,26,15,30,17,34,19,38,20,40,
%T A258046 21,42,22,44,23,46,24,48,31,27,54,25,50,41,29,58,28,56,32,64,33,66,39,
%U A258046 43,35,70,37,74,49,98,45,90,47,94,52,104,53,106,51,102
%N A258046 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.
%C A258046 Rule 3 follows.  For k >= 1, let  A(k) = {a(1), …, a(k)} and D(k) = {d(1), …, d(k)}.  Begin with k = 1 and nonnegative integers a(1) and d(1).
%C A258046 Step 1:   If there is an integer h such that 1 - a(k) < h < 0 and h is not in D(k) and a(k) + h is not in A(k), let d(k+1) be the least such h, let a(k+1) = a(k) + h, replace k by k + 1, and repeat Step 1; otherwise do Step 2.
%C A258046 Step 2:  Let h be the least positive integer not in D(k) such that a(k) - h is not in A(k).  Let a(k+1) = a(k) + h and d(k+1) = h.  Replace k by k+1 and do Step 1.
%C A258046 See A257905 for a guide to related sequences and conjectures.
%H A258046 Clark Kimberling, <a href="/A258046/b258046.txt">Table of n, a(n) for n = 1..1000</a>
%e A258046 a(1) = 1, d(1) = 0;
%e A258046 a(2) = 2, d(2) = 1;
%e A258046 a(3) = 4, d(3) = 2;
%e A258046 a(4) = 3, d(4) = -1.
%t A258046 {a, f} = {{1}, {0}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A258046 If[! IntegerQ[tmp[[1]]], tmp = {Last[a] + #, #} &[NestWhile[# + 1 &, 1, ! (! MemberQ[f, #] && ! MemberQ[a, Last[a] - #]) &]]]; AppendTo[a, tmp[[1]]]; AppendTo[f, tmp[[2]]], {120}]; {a, f} (* _Peter J. C. Moses_, May 14 2015 *)
%Y A258046 Cf. A257905, A258047, A256283, A258049, A258050.
%K A258046 nonn,easy
%O A258046 1,2
%A A258046 _Clark Kimberling_, Jun 03 2015