A392661 Upper Wythoff partition sequence of the triangular numbers (A003086); see A392660.

3, 10, 21, 45, 55, 91, 120, 153, 190, 231, 276, 351, 406, 435, 528, 630, 666, 741, 820, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1830, 1953, 2080, 2211, 2346, 2485, 2628, 2775, 3003, 3160, 3321, 3486, 3741, 3828, 4005, 4186, 4465, 4656, 4753, 5050

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Mathematica

Clear[generateSequenceFast];
s = Range[200]*(1 + Range[200])/2  (* User: put your sequence s here.*)
generateSequenceFast[seq_] := Module[{seqLen = Length[seq], used, a, b, n = 1, pa = 1, pb = 1, bTarget}, used = ConstantArray[False, seqLen];
   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]
First[u]   (* A392660*)
Last[u]    (* A392661*)
(* Peter J. C. Moses, Dec 23 2025 *)

Crossrefs

Cf. A000040, A000201, A001950, A000217, A392117, A392656, A392660, A392663.

Sequence in context: A117495 A007687 A330273 * A335666 A192033 A295063

Adjacent sequences: A392658 A392659 A392660 * A392662 A392663 A392664

Keyword

nonn

Author

Clark Kimberling, Feb 22 2026

Status

approved