A195872 Positive integers a for which there is a (-1/2)-Pythagorean triple (a,b,c) satisfying a<=b.
1, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 26
Offset: 1
Keywords
Examples
(-1/2)-Pythagorean triples: 1,2,2 2,4,4 3,6,6 4,8,8 5,48,47 (For primitive triples, see A195875.)
Programs
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Mathematica
z8 = 800; z9 = 400; z7 = 100; k = -1/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b]; d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0] t[a_] := Table[d[a, b], {b, a, z8}] u[n_] := Delete[t[n], Position[t[n], 0]] Table[u[n], {n, 1, 15}] t = Table[u[n], {n, 1, z8}]; Flatten[Position[t, {}]] u = Flatten[Delete[t, Position[t, {}]]]; x[n_] := u[[3 n - 2]]; Table[x[n], {n, 1, z7}] (* A195872 *) y[n_] := u[[3 n - 1]]; Table[y[n], {n, 1, z7}] (* A195873 *) z[n_] := u[[3 n]]; Table[z[n], {n, 1, z7}] (* A195874 *) x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0] y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0] z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0] f = Table[x1[n], {n, 1, z9}]; x2 = Delete[f, Position[f, 0]] (* A195875 *) g = Table[y1[n], {n, 1, z9}]; y2 = Delete[g, Position[g, 0]] (* A195876 *) h = Table[z1[n], {n, 1, z9}]; z2 = Delete[h, Position[h, 0]] (* A195877 *)
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