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A257987 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 2 and d(1) = 2.

%I A257987 #7 Jun 16 2015 13:54:50
%S A257987 2,3,6,4,8,5,10,9,17,7,13,25,11,21,12,23,15,29,14,27,16,31,18,35,19,
%T A257987 37,20,39,32,26,22,43,24,47,42,30,59,28,55,33,65,36,71,34,67,40,79,38,
%U A257987 75,41,81,45,89,44,87,48,95,46,91,49,97,50,99,51,101,57
%N A257987 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 2 and d(1) = 2.
%C A257987 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 A257987 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 A257987 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 A257987 See A257905 for a guide to related sequences and conjectures.
%H A257987 Clark Kimberling, <a href="/A257987/b257987.txt">Table of n, a(n) for n = 1..1000</a>
%F A257987 a(n) - a(n-1) = A257984(n) for n >= 2.
%e A257987 a(1) = 2, d(1) = 2;
%e A257987 a(2) = 3, d(2) = 1;
%e A257987 a(3) = 6, d(3) = 3;
%e A257987 a(4) = 4, d(4) = -2.
%t A257987 {a, f} = {{2}, {2}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A257987 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 A257987 Cf. A257905, A257909.
%K A257987 nonn,easy
%O A257987 1,1
%A A257987 _Clark Kimberling_, Jun 02 2015