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A258047 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

%I A258047 #7 Jun 16 2015 13:55:00
%S A258047 0,1,2,-1,3,6,-7,5,-3,7,-6,8,-5,-2,9,18,-23,13,-11,15,-13,17,-15,19,
%T A258047 -18,20,-19,21,-20,22,-21,23,-22,24,-17,-4,27,-29,25,-9,-12,29,-30,28,
%U A258047 -24,32,-31,33,-27,4,-8,35,-33,37,-25,49,-53,45,-43,47,-42,52
%N A258047 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.
%C A258047 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 A258047 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 A258047 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 A258047 See A257905 for a guide to related sequences and conjectures.
%H A258047 Clark Kimberling, <a href="/A258047/b258047.txt">Table of n, a(n) for n = 1..1000</a>
%e A258047 a(1) = 1, d(1) = 0;
%e A258047 a(2) = 2, d(2) = 1;
%e A258047 a(3) = 4, d(3) = 2;
%e A258047 a(4) = 3, d(4) = -1.
%t A258047 {a, f} = {{1}, {0}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A258047 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 A258047 Cf. A257905, A258046, A258049, A258050.
%K A258047 easy,sign
%O A258047 1,3
%A A258047 _Clark Kimberling_, Jun 05 2015