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A257910 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 3.

%I A257910 #9 Jun 05 2015 03:42:07
%S A257910 0,1,3,2,6,4,9,5,11,8,17,7,15,10,21,12,25,13,27,14,29,18,37,16,33,19,
%T A257910 39,20,41,23,47,22,45,28,57,24,49,26,53,31,63,32,65,30,61,34,69,35,71,
%U A257910 42,36,73,43,87,38,77,40,81,55,48,97,44,89,46,93,51,103
%N A257910 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 3.
%C A257910 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 A257910 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 A257910 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 A257910 See A257905 for a guide to related sequences and conjectures.
%H A257910 Clark Kimberling, <a href="/A257910/b257910.txt">Table of n, a(n) for n = 1..1000</a>
%e A257910 a(1) = 0, d(1) = 3;
%e A257910 a(2) = 1, d(2) = 1;
%e A257910 a(3) = 3, d(3) = 2;
%e A257910 a(4) = 2, d(4) = -1.
%t A257910 {a, f} = {{0}, {3}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t A257910 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 A257910 Cf. A257905, A257980.
%K A257910 nonn,easy
%O A257910 1,3
%A A257910 _Clark Kimberling_, May 16 2015