A242286 Positive integers k for which the k-th triangular number is greedy-summable.

4, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 72, 73, 75, 76, 77, 78, 79, 81, 82, 84, 85, 87, 88, 89, 91, 92, 94, 95

Offset

1,1

Comments

Greedy summability is defined at A242284.

Links

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

Example

Let s(n) = n(n+1)/2 = A000217(n).  Then
a(1) = 4; s(4) = 10 = 6 + 3 + 1;
a(2) = 6; s(6) = 21 = 15 + 6;
a(3) = 7; s(7) = 28 = 21 + 6 + 1;
a(4) = 9; s(9) = 45 = 36 + 6 + 3.

Mathematica

z = 200;  s = Table[n (n + 1)/2, {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]
r[n_] := s[[n]] - Total[t[[n]][[2]]];
tr = Table[r[n], {n, 2, z}]  (* A242284 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242285 *)
f = 1 + Flatten[Position[tr, 0]]  (* A242286 *)
f (f + 1)/2  (* A242287 *) (* Peter J. C. Moses, May 06 2014 *)

Crossrefs

Cf. A242284, A242285, A242287, A241833, A000217.

Sequence in context: A288383 A001690 A105447 * A144222 A010414 A254122

Adjacent sequences: A242283 A242284 A242285 * A242287 A242288 A242289

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved