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%I #4 Jun 05 2015 03:42:33
%S 1,2,-1,3,5,-6,4,-2,6,-5,7,-3,11,-13,9,18,-23,13,-11,15,-14,16,-15,17,
%T -10,-4,20,-21,19,-17,21,-19,23,-18,28,-31,25,-9,-12,29,-27,31,-35,27,
%U -7,-8,39,-45,33,-29,37,-39,35,-26,44,-43,45,-47,43,-38,48
%N Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 1.
%C 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 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 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 See A257905 for a guide to related sequences and conjectures.
%H Clark Kimberling, <a href="/A257982/b257982.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 1, d(1) = 1;
%e a(2) = 3, d(2) = 2;
%e a(3) = 2, d(3) = -1;
%e a(4) = 5, d(4) = 3.
%t {a, f} = {{1}, {1}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
%t 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 Cf. A257905, A257981.
%K sign,easy
%O 1,2
%A _Clark Kimberling_, May 19 2015
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