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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 February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)