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A242286 Positive integers k for which the k-th triangular number is greedy-summable. 4

%I

%S 4,6,7,9,10,11,13,14,15,16,18,19,21,22,24,25,27,28,29,31,32,34,35,36,

%T 37,39,40,42,43,45,46,48,49,51,52,54,55,56,58,59,61,62,64,65,66,67,69,

%U 70,72,73,75,76,77,78,79,81,82,84,85,87,88,89,91,92,94,95

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

%C Greedy summability is defined at A242284.

%H Clark Kimberling, <a href="/A242286/b242286.txt">Table of n, a(n) for n = 1..1000</a>

%e Let s(n) = n(n+1)/2 = A000217(n). Then

%e a(1) = 4; s(4) = 10 = 6 + 3 + 1;

%e a(2) = 6; s(6) = 21 = 15 + 6;

%e a(3) = 7; s(7) = 28 = 21 + 6 + 1;

%e a(4) = 9; s(9) = 45 = 36 + 6 + 3.

%t 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}]

%t r[n_] := s[[n]] - Total[t[[n]][[2]]];

%t tr = Table[r[n], {n, 2, z}] (* A242284 *)

%t c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242285 *)

%t f = 1 + Flatten[Position[tr, 0]] (* A242286 *)

%t f (f + 1)/2 (* A242287 *) (* _Peter J. C. Moses_, May 06 2014 *)

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

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 10 2014

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)