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A257986 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 2 and d(1) = 1.

%I A257986 #4 Jun 05 2015 03:42:56
%S A257986 2,4,3,6,11,5,9,7,13,8,15,12,23,10,19,37,14,27,16,31,17,33,18,35,25,
%T A257986 21,41,20,39,22,43,24,47,29,57,26,51,42,30,59,32,63,28,55,48,40,79,34,
%U A257986 67,38,75,36,71,45,89,46,91,44,87,49,97,53,105,50,99,58
%N A257986 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 2 and d(1) = 1.
%C A257986 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 A257986 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 A257986 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 A257986 See A257905 for a guide to related sequences and conjectures.
%H A257986 Clark Kimberling, <a href="/A257986/b257986.txt">Table of n, a(n) for n = 1..1000</a>
%F A257986 a(n) - a(n-1) = A257982(n) for n >= 2.
%e A257986 a(1) = 2, d(1) = 1;
%e A257986 a(2) = 4, d(2) = 2;
%e A257986 a(3) = 3, d(3) = -1;
%e A257986 a(4) = 6, d(4) = 3.
%t A257986 {a, f} = {{2}, {1}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A257986 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 A257986 Cf. A257905, A257982.
%K A257986 nonn,easy
%O A257986 1,1
%A A257986 _Clark Kimberling_, Jun 02 2015