The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A257912 Sequence (d(n)) generated by Algorithm (in Comments) with a(1) = 2 and d(1) = 2. 3
 2, -1, 3, 1, -2, 4, 5, -6, 7, -5, 6, -4, 8, -9, 10, -8, 9, -3, 11, -13, 12, -11, 13, -7, 14, -15, 16, -14, 15, -12, 17, -19, 18, -17, 19, -10, 20, -24, 21, -20, 22, -21, 23, -22, 24, -18, 25, -29, 26, -16, 27, -32, 28, -27, 29, -23, 30, -31, 32, -30, 31, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 MATHEMATICA a[1] = 2; d[1] = 2; 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}]; Table[a[k], {k, 1, zz}] (* A257911 *) Table[d[k], {k, 1, zz}] (* A257912 *) CROSSREFS Cf. A257911, A257883. Sequence in context: A045898 A303754 A257918 * A036262 A080521 A169613 Adjacent sequences: A257909 A257910 A257911 * A257913 A257914 A257915 KEYWORD easy,sign AUTHOR Clark Kimberling, Jun 12 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 12:13 EDT 2024. Contains 373331 sequences. (Running on oeis4.)