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 A256795 Difference sequence of A256793. 2
 1, 2, 3, 2, 2, 3, 3, 1, 2, 3, 3, 2, 1, 2, 3, 3, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 3, 3, 1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 3, 3, 1, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are the numbers of consecutive positive traces when the minimal alternating squares representations for positive integers are written in order. Is every term < 5? The first term greater than 3 is a(116) = 4, corresponding to these 3 consecutive representations: R(225) = 225; R(226) = 256 - 36 + 9 - 4 + 1; R(227) = 256 - 36 + 9 - 4 + 2. (See A256789 for definitions.) LINKS Table of n, a(n) for n=1..86. MATHEMATICA b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}]; (* Squares as base *) s[n_] := Table[b[n], {k, 1, 2 n - 1}]; h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]; Table[r[n], {n, 0, 120}]; (* A256789 *) u = Flatten[Table[Last[r[n]], {n, 1, 1000}]]; (* A256791 *) u1 = Select[Range[800], u[[#]] > 0 &]; (* A256792 *) u2 = Select[Range[800], u[[#]] < 0 &]; (* A256793 *) Differences[u1] (* A256794 *) Differences[u2] (* A256795 *) CROSSREFS Cf. A256792, A256794. Sequence in context: A282900 A126014 A317420 * A273404 A281976 A300708 Adjacent sequences: A256792 A256793 A256794 * A256796 A256797 A256798 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 13 2015 STATUS approved

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)