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 A257884 Sequence (a(n)) generated by Algorithm (in Comments) with a(1) = 0 and d(1) = 1. 3
 0, 2, 1, 4, 8, 3, 9, 5, 10, 7, 14, 6, 15, 13, 21, 11, 22, 16, 26, 12, 24, 17, 30, 18, 32, 19, 34, 23, 39, 20, 37, 28, 46, 25, 44, 27, 47, 29, 50, 35, 57, 31, 54, 38, 62, 33, 58, 36, 63, 40, 66, 41, 69, 42, 71, 43, 73, 49, 80, 45, 77, 110, 48, 82, 51, 86, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Algorithm:  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).  Let h be the least integer > -a(k) such that h is not in D(k) and 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 repeat inductively. Conjecture:  if a(1) is an nonnegative integer and d(1) is an integer, then (a(n)) is a permutation of the nonnegative integers (if a(1) = 0) or a permutation of the positive integers (if a(1) > 0).  Moreover, (d(n)) is a permutation of the integers if d(1) = 0, or of the nonzero integers if d(1) > 0. See A257883 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 FORMULA a(k+1) - a(k) = d(k+1) for k >= 1. EXAMPLE a(1) = 0, d(1) = 1; a(2) = 2, d(2) = 2; a(3) = 1, d(3) = -1; a(4) = 4, d(4) = 3. MATHEMATICA a[1] = 0; d[1] = 1; k = 1; z = 10000; zz = 120; A[k_] := Table[a[i], {i, 1, k}]; diff[k_] := Table[d[i], {i, 1, k}]; c[k_] := Complement[Range[-z, z], diff[k]]; T[k_] := -a[k] + Complement[Range[z], A[k]] Table[{h = Min[Intersection[c[k], T[k]]], a[k + 1] = a[k] + h,    d[k + 1] = h, k = k + 1}, {i, 1, zz}]; u = Table[a[k], {k, 1, zz}]  (* A257884 *) Table[d[k], {k, 1, zz}]      (* A175499 *) CROSSREFS Cf. A257883, A175498, A257705, A081145. Sequence in context: A094511 A209060 A193730 * A026204 A059146 A059148 Adjacent sequences:  A257881 A257882 A257883 * A257885 A257886 A257887 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 13 2015 STATUS approved

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)