A256789 -id:A256789 - cp's OEIS frontend

A256797 Nonpositive part of the minimal alternating squares representation of n.

0, 2, 1, 0, 4, 4, 4, 1, 0, 10, 9, 4, 4, 4, 1, 0, 9, 11, 10, 9, 4, 4, 4, 1, 0, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 16, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4

Offset: 1

Clark Kimberling, Apr 13 2015

See A256789 for definitions.

			R(1) = 1, positive part 1, nonpositive part 0;
R(2) = 4 - 2, positive part 4, nonpositive part 2;
R(3) = 4 - 1, positive part 4, nonpositive part 1;
R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A256789, A256796.

b[n_] := n^2; bb = Table[b[n], {n, 0, 100}];
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]]];
t = Table[r[n], {n, 1, z}] (* A256789 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256796 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256797 *)

A256798 Numbers whose minimal alternating squares representation has trace 2 or -2.

Original entry on oeis.org

2, 7, 14, 18, 23, 29, 34, 42, 47, 50, 57, 62, 67, 74, 79, 82, 86, 93, 98, 103, 107, 114, 119, 126, 130, 137, 142, 146, 151, 155, 162, 167, 173, 178, 182, 189, 194, 202, 207, 211, 218, 223, 227, 233, 238, 242, 249, 254, 260, 266, 271, 275, 282, 287, 290, 295

Offset: 1

Clark Kimberling, Apr 13 2015

The trace of all other positive integers is h^2 or -h^2 for some integer h. (See A256789 for definitions and A256791 for traces.)

			Trace(n) = 2 for n = 7, 14, 23, 34, 47, 62, ..
Trace(n) = -2 for n = 2, 18, 29, 42, 50, 57, 67, ...
Together in increasing order:  2, 7, 14, 18, 23, 29, 34, 42, ...

Cf. A256789, A256791.

b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
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 *)
Select[Range[800], Abs[u[[#]]] == 2 &] (* A256798 *)

cp's OEIS Frontend

A256797 Nonpositive part of the minimal alternating squares representation of n.

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