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

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

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Links

• 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.

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

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