A258049 -id:A258049 - cp's OEIS frontend

A258047 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

0, 1, 2, -1, 3, 6, -7, 5, -3, 7, -6, 8, -5, -2, 9, 18, -23, 13, -11, 15, -13, 17, -15, 19, -18, 20, -19, 21, -20, 22, -21, 23, -22, 24, -17, -4, 27, -29, 25, -9, -12, 29, -30, 28, -24, 32, -31, 33, -27, 4, -8, 35, -33, 37, -25, 49, -53, 45, -43, 47, -42, 52

Offset: 1

Clark Kimberling, Jun 05 2015

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.

			a(1) = 1, d(1) = 0;
a(2) = 2, d(2) = 1;
a(3) = 4, d(3) = 2;
a(4) = 3, d(4) = -1.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A257905, A258046, A258049, A258050.

{a, f} = {{1}, {0}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
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 *)

A258050 Position of -n in A258047 after deleting the initial 0.

Original entry on oeis.org

3, 6, 8, 10, 12, 13, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 35, 37, 39, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124

Offset: 1

Clark Kimberling, Jun 05 2015

A258047 = (0,1,2,-1,3,6,-7,5,-3,7,...). Remove the initial 0 to get (1,2,-1,3,6,-7,5,6,-3,7,...), and note that (1,2,3,4,...) occupy positions 1,2,4,7,..., (as in A258049) and that (-1,-2,-3,...) occupy positions 3,6,8,... (as in A258050).

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A258047, A258049 (complement).

{a, f} = {{1}, {0}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
If[! IntegerQ[tmp[[1]]], tmp = {Last[a] + #, #} &[NestWhile[# + 1 &, 1, ! (! MemberQ[f, #] && ! MemberQ[a, Last[a] - #]) &]]];
AppendTo[a, tmp[[1]]]; AppendTo[f, tmp[[2]]], {500}];
-1 + Flatten[Position[Sign[f], 1]]  (* A258049 *)
-1 + Flatten[Position[Sign[f], -1]] (* A258050 *) (* Peter J. C. Moses, May 14 2015 *)

A258046 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

Original entry on oeis.org

1, 2, 4, 3, 6, 12, 5, 10, 7, 14, 8, 16, 11, 9, 18, 36, 13, 26, 15, 30, 17, 34, 19, 38, 20, 40, 21, 42, 22, 44, 23, 46, 24, 48, 31, 27, 54, 25, 50, 41, 29, 58, 28, 56, 32, 64, 33, 66, 39, 43, 35, 70, 37, 74, 49, 98, 45, 90, 47, 94, 52, 104, 53, 106, 51, 102

Offset: 1

Clark Kimberling, Jun 03 2015

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.

			a(1) = 1, d(1) = 0;
a(2) = 2, d(2) = 1;
a(3) = 4, d(3) = 2;
a(4) = 3, d(4) = -1.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A257905, A258047, A256283, A258049, A258050.

{a, f} = {{1}, {0}}; Do[tmp = {#, # - Last[a]} &[Min[Complement[#, Intersection[a, #]]&[Last[a] + Complement[#, Intersection[f, #]] &[Range[2 - Last[a], -1]]]]];
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 *)

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A258047 Sequence (d(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

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A258050 Position of -n in A258047 after deleting the initial 0.

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A258046 Sequence (a(n)) generated by Rule 3 (in Comments) with a(1) = 1 and d(1) = 0.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica