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 A196155 Positive integers a for which there is a 5-Pythagorean triple (a,b,c) satisfying a<=b. 7
 1, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences. LINKS Table of n, a(n) for n=1..73. MATHEMATICA z8 = 900; z9 = 250; z7 = 200; k = 5; 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}] (* A196155 *) y[n_] := u[[3 n - 1]]; Table[y[n], {n, 1, z7}] (* A196156 *) z[n_] := u[[3 n]]; Table[z[n], {n, 1, z7}] (* A196157 *) 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]] (* A196158 *) g = Table[y1[n], {n, 1, z9}]; y2 = Delete[g, Position[g, 0]] (* A196159 *) h = Table[z1[n], {n, 1, z9}]; z2 = Delete[h, Position[h, 0]] (* A196160 *) CROSSREFS Cf. Ac. A195770, A196155, A196156, A196158. Sequence in context: A238690 A332299 A229835 * A140858 A075458 A332271 Adjacent sequences: A196152 A196153 A196154 * A196156 A196157 A196158 KEYWORD nonn AUTHOR Clark Kimberling, Sep 28 2011 STATUS approved

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Last modified June 3 23:57 EDT 2023. Contains 363118 sequences. (Running on oeis4.)