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 A257980 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 0 and d(1) = 3. 3
 3, 1, 2, -1, 4, -2, 5, -4, 6, -3, 9, -10, 8, -5, 11, -9, 13, -12, 14, -13, 15, -11, 19, -21, 17, -14, 20, -19, 21, -18, 24, -25, 23, -17, 29, -33, 25, -23, 27, -22, 32, -31, 33, -35, 31, -27, 35, -34, 36, -29, -6, 37, -30, 44, -49, 39, -37, 41, -26, -7, 49 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). 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. 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. See A257905 for a guide to related sequences and conjectures. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE a(1) = 0, d(1) = 3; a(2) = 1, d(2) = 1; a(3) = 3, d(3) = 2; a(4) = 2, d(4) = -1. MATHEMATICA {a, f} = {{0}, {3}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]]; If[! IntegerQ[tmp[]], tmp = {Last[a] + #, #} &[NestWhile[# + 1 &, 1, ! (! MemberQ[f, #] && ! MemberQ[a, Last[a] - #]) &]]]; AppendTo[a, tmp[]]; AppendTo[f, tmp[]], {120}]; {a, f} (* Peter J. C. Moses, May 14 2015 *) CROSSREFS Cf. A257905, A257910. Sequence in context: A066743 A257915 A257904 * A203531 A324885 A046645 Adjacent sequences:  A257977 A257978 A257979 * A257981 A257982 A257983 KEYWORD easy,sign AUTHOR Clark Kimberling, May 19 2015 STATUS approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)