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A195879
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Positive integers a for which there is a (1/2)-Pythagorean triple (a,b,c) satisfying a<=b.
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7
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2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 24, 24, 25, 25, 26, 26, 26, 26, 26, 27, 27, 28, 28, 28, 28, 29, 29, 30, 30, 30, 30, 31
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OFFSET
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1,1
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COMMENTS
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See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
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LINKS
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Table of n, a(n) for n=1..70.
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MATHEMATICA
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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}] (* A195879 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}] (* A195880 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}] (* A195881 *)
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]] (* A195882 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]] (* A195883 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]] (* A195884 *)
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CROSSREFS
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Cf. A195770, A195880, A195882.
Sequence in context: A080680 A005376 A196362 * A216522 A086419 A025548
Adjacent sequences: A195876 A195877 A195878 * A195880 A195881 A195882
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Sep 25 2011
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STATUS
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approved
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