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 A242305 Squares-greedy residue of n. 3
 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Suppose that s = (s(1), s(2), ... ) is a sequence of real numbers such that for every real number u, at most finitely many s(i) are < u, and suppose that x > min(s).  We shall apply the greedy algorithm to x, using terms of s.  Specifically, let i(1) be an index i such that s(i) = max{s(j) < x}, and put d(1) = x - s(i(1)).  If d(1) < s(i) for all i, put r = x - s(i(1)).  Otherwise, let i(2) be an index i such that s(i) = max{s(j) < x - s(i(1))}, and put d(2) = x - s(i(1)) - s(i(2)).  If d(2) < s(i) for all i, put r = x - s(i(1)) - s(i(2)).  Otherwise, let i(3) be an index i such that s(i) = max{s(j) < x - s(i(1)) - s(i(2))}, and put d(3) = x - s(i(1)) - s(i(2)) - s(i(3)).  Continue until reaching k such that d(k) < s(i) for every i, and put r = x - s(i(1)) - ... - s(i(k)).  Call r the s-greedy residue of x, and call s(i(1)) + ... + s(i(k)) the s-greedy sum for x.   If r = 0, call x s-greedy summable. LINKS Clark Kimberling, Table of n, a(n) for n = 2..2000 EXAMPLE n ... a(n) 1 ... (undefined) 2 ... 1 = 2 - 1 3 ... 2 = 3 - 1 4 ... 3 = 4 - 1 5 ... 0 = 5 - 4 - 1 6 ... 1 = 6 - 4 - 1 7 ... 2 = 7 - 4 - 1 8 ... 3 = 8 - 4 - 1 9 ... 4 = 9 - 4 - 1 10 .. 0 = 10 - 9 - 1 11 .. 1 = 11 - 9 - 1 12 .. 2 = 12 - 9 - 1 13 .. 0 = 13 - 9 - 4 MATHEMATICA z = 200;  s = Table[n^2, {n, 1, z}]; s1 = Table[n, {n, 1, z}]; t = Table[{s1[[n]], #, Total[#] == s1[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s1[[n]], Reverse[Select[s, # < s1[[n]] &]]]], 0]], {n, z}] r[n_] := s1[[n]] - Total[t[[n]][[2]]]; tr = Table[r[n], {n, 2, z}]  (* A242305 *) c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242306 *) f = 1 + Flatten[Position[tr, 0]]  (* A242307 *)  (* Peter J. C. Moses, May 06 2014 *) CROSSREFS Cf. A242306, A242307, A241833, A000027, A000290. Sequence in context: A277904 A132387 A124757 * A049263 A014588 A293497 Adjacent sequences:  A242302 A242303 A242304 * A242306 A242307 A242308 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 11 2014 STATUS approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)