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A257908 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 2.

%I A257908 #9 Jun 05 2015 03:41:44
%S A257908 0,1,4,2,6,3,8,7,15,5,11,23,9,19,10,21,13,27,12,25,14,29,16,33,17,35,
%T A257908 18,37,30,24,20,41,22,45,40,28,57,26,53,31,63,34,69,32,65,38,77,36,73,
%U A257908 39,79,43,87,42,85,46,93,44,89,47,95,48,97,49,99,55,111
%N A257908 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 2.
%C A257908 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 A257908 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 A257908 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 A257908 See A257905 for a guide to related sequences and conjectures.
%H A257908 Clark Kimberling, <a href="/A257908/b257908.txt">Table of n, a(n) for n = 1..1000</a>
%e A257908 a(1) = 0, d(1) = 2;
%e A257908 a(2) = 1, d(2) = 1;
%e A257908 a(3) = 4, d(3) = 3;
%e A257908 a(4) = 2, d(4) = -2.
%t A257908 {a, f} = {{0}, {2}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A257908 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 A257908 Cf. A257905, A257909.
%K A257908 nonn,easy
%O A257908 1,3
%A A257908 _Clark Kimberling_, May 16 2015