A256798 - OEIS

%I #6 Apr 14 2015 11:05:36

%S 2,7,14,18,23,29,34,42,47,50,57,62,67,74,79,82,86,93,98,103,107,114,

%T 119,126,130,137,142,146,151,155,162,167,173,178,182,189,194,202,207,

%U 211,218,223,227,233,238,242,249,254,260,266,271,275,282,287,290,295

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

%C 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.)

%e Trace(n) = 2 for n = 7, 14, 23, 34, 47, 62, ..

%e Trace(n) = -2 for n = 2, 18, 29, 42, 50, 57, 67, ...

%e Together in increasing order:  2, 7, 14, 18, 23, 29, 34, 42, ...

%t b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];

%t s[n_] := Table[b[n], {k, 1, 2 n - 1}];

%t h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];

%t g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];

%t Table[r[n], {n, 0, 120}]  (* A256789 *)

%t u = Flatten[Table[Last[r[n]], {n, 1, 1000}]]; (* A256791 *)

%t Select[Range[800], Abs[u[[#]]] == 2 &] (* A256798 *)

%Y Cf. A256789, A256791.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Apr 13 2015