A392663 Indices of the upper Wythoff partition sequence of the triangular numbers; see A392660.

2, 4, 6, 9, 10, 13, 15, 17, 19, 21, 23, 26, 28, 29, 32, 35, 36, 38, 40, 43, 45, 47, 49, 51, 53, 55, 57, 60, 62, 64, 66, 68, 70, 72, 74, 77, 79, 81, 83, 86, 87, 89, 91, 94, 96, 97, 100, 103, 105, 106, 108, 112, 113, 115, 117, 119, 122, 124, 125, 127, 130, 132

Offset

1,1

Comments

The sequences A392662 and A392663 partition the positive integers, A000027.

Links

Table of n, a(n) for n=1..62.

Formula

A003056(A392661).

Mathematica

generateSequenceFast[seq_] := Module[{seqLen = Length[seq], used, a, b, n = 1, pa = 1, pb = 1, bTarget}, used = ConstantArray[False, seqLen];
   s = Range[200]*(1 + Range[200])/2; (* User: put your sequence s here. *)
   a = ConstantArray[0, seqLen];
   b = a; a[[1]] = seq[[1]]; used[[1]] = True;
   While[n <= seqLen, bTarget = a[[n]] + seq[[n]];
    While[pb <= seqLen && (used[[pb]] || seq[[pb]] < bTarget), pb++];
    If[pb > seqLen, Break[]];
    b[[n]] = seq[[pb]]; used[[pb]] = True; pa = Max[pa, 2];
    While[pa <= seqLen && used[[pa]], pa++];
    If[pa > seqLen, Break[]]; a[[n + 1]] = seq[[pa]]; used[[pa]] = True; n++];
   {Take[a, n], Take[b, n - 1]}];
u = generateSequenceFast[s]
s1 = First[u]   (* A392660 *)
s2 = Last[u]   (* A392661 *)
w = Sort[Join[s1, s2]]
Flatten[Flatten[Position[w, #]] & /@s1] (* A392662 *)
Flatten[Flatten[Position[w, #]] & /@s2] (* A392663 *)
(* Peter J. C. Moses, Dec 23 2025 *)

Crossrefs

Cf. A000040, A000201, A001950, A000217, A392117, A392656, A392660, A392662.

Sequence in context: A138972 A050110 A392659 * A184416 A187225 A003661

Adjacent sequences: A392660 A392661 A392662 * A392664 A392665 A392666

Keyword

nonn

Author

Clark Kimberling, Feb 23 2026

Status

approved