A256795 Difference sequence of A256793.

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

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