A026139 -id:A026139 - cp's OEIS frontend

A026141 a(n) = (s(n)-s(n-1))/2, where s = A026139.

1, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 1, 3, 3, 2, 1, 3, 2, 1

Offset: 2

Clark Kimberling

nonn

Michael De Vlieger, Table of n, a(n) for n = 2..10002
F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020.

Cf. A026136, A026139.

Block[{a, r, s, nn = 105}, a[1] = 1; Do[If[! IntegerQ[a[#1]], Set[a[#1], i], Set[a[#2], i]] & @@ {i - #, i + #} &@ Floor[i/2], {i, 4 nn}]; s = TakeWhile[Array[a[#] &, 2 nn], IntegerQ]; Map[(#2 - #1)/2 & @@ # &, Partition[Union@ FoldList[Max, s], 2, 1]]] (* Michael De Vlieger, Aug 27 2021 *)

Edited by N. J. A. Sloane, Jan 31 2020

A026140 a(n) = (1/2)*(s(n) - 1), where s = A026139.

Original entry on oeis.org

0, 1, 3, 4, 7, 9, 10, 12, 13, 16, 19, 21, 22, 25, 27, 28, 30, 31, 34, 36, 37, 39, 40, 43, 46, 48, 49, 52, 55, 57, 58, 61, 63, 64, 66, 67, 70, 73, 75, 76, 79, 81, 82, 84, 85, 88, 90, 91, 93, 94, 97, 100, 102, 103, 106, 108, 109, 111, 112, 115, 117, 118

Offset: 1

Clark Kimberling

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..5004

Cf. A026136, A026139.

Block[{a, r, s, nn = 119}, a[1] = 1; Do[If[! IntegerQ[a[#1]], Set[a[#1], i], Set[a[#2], i]] & @@ {i - #, i + #} &@ Floor[i/2], {i, 2 nn}]; s = TakeWhile[Array[a[#] &, 2 nn], IntegerQ]; Map[(1/2) (# - 1) &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Aug 27 2021 *)

A026175 Duplicate of A026139.

Original entry on oeis.org

1, 3, 7, 9, 15, 19, 21, 25, 27, 33, 39, 43, 45, 51, 55, 57, 61, 63, 69, 73, 75, 79, 81, 87, 93, 97, 99, 105, 111, 115, 117, 123, 127, 129, 133, 135, 141, 147, 151, 153, 159, 163, 165, 169, 171, 177, 181, 183, 187, 189, 195, 201, 205, 207

Offset: 1

dead

A026138 Numbers k such that s(j) < s(k) for all j < k, where s = A026136.

Original entry on oeis.org

1, 2, 4, 5, 8, 10, 11, 13, 14, 17, 20, 22, 23, 26, 28, 29, 31, 32, 35, 37, 38, 40, 41, 44, 47, 49, 50, 53, 56, 58, 59, 62, 64, 65, 67, 68, 71, 74, 76, 77, 80, 82, 83, 85, 86, 89, 91, 92, 94, 95, 98, 101, 103, 104, 107, 109, 110, 112, 113

Offset: 1

Clark Kimberling

nonn

Also a(n) = (1/2)*s(n+1), where s = A026169.
That these definitions produce the same sequence can be established using the methods in the Dekking paper.
Indices of records in A026136. - Michael De Vlieger, Aug 27 2021

Michael De Vlieger, Table of n, a(n) for n = 1..10000
F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020.

Cf. A026136, A026139 (records in A026136), A026169.

Block[{a, r, s, nn = 113}, a[1] = 1; Do[If[! IntegerQ[a[#1]], Set[a[#1], i], Set[a[#2], i]] & @@ {i - #, i + #} &@ Floor[i/2], {i, 2 nn}]; s = TakeWhile[Array[a[#] &, nn], IntegerQ]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Aug 27 2021 *)

Edited by N. J. A. Sloane, Jan 31 2020

cp's OEIS Frontend

A026141 a(n) = (s(n)-s(n-1))/2, where s = A026139.

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A026140 a(n) = (1/2)*(s(n) - 1), where s = A026139.

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A026175 Duplicate of A026139.

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A026138 Numbers k such that s(j) < s(k) for all j < k, where s = A026136.

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