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A256793
Numbers whose minimal alternating squares representation has positive trace.
4
2, 3, 5, 8, 10, 12, 15, 18, 19, 21, 24, 27, 29, 30, 32, 35, 38, 40, 42, 43, 45, 48, 50, 51, 53, 55, 57, 58, 60, 63, 65, 67, 68, 70, 72, 74, 75, 77, 80, 83, 84, 86, 87, 89, 91, 93, 94, 96, 99, 101, 104, 105, 107, 108, 110, 112, 114, 115, 117, 120, 122, 124
OFFSET
1,1
COMMENTS
See A256789 for definitions.
LINKS
EXAMPLE
R(1) = 1; trace = 1, positive.
R(2) = 4 - 2; trace = -2, negative.
R(3) = 4 - 1; trace = -1, negative.
MATHEMATICA
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], u[[#]] > 0 &] (* A256792 *)
Select[Range[800], u[[#]] < 0 &] (* A256793 *)
CROSSREFS
Cf. A256789, A256792 (complement).
Sequence in context: A277625 A098177 A223577 * A193640 A112045 A098389
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 13 2015
STATUS
approved