A196259 Positive integers a in (1/4)-Pythagorean triples (a,b,c) satisfying a<=b, in order of increasing a and then increasing b.
2, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 18, 19, 20, 20, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 28, 28, 28, 28, 28, 29, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
F:= proc(a) sort(select(t -> subs(t,b) >= a and subs(t,c) > 0, [isolve](4*a^2 + 4*b^2 + a*b = 4*c^2)),(s,t) -> subs(s,b) <= subs(t,b)) end proc: seq(a$nops(F(a)), a=1..40); # Robert Israel, Dec 18 2024
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Mathematica
(* Warning: this code is incorrect, as it imposes a limit b <= 900 *) z8 = 900; z9 = 250; z7 = 200; k = 1/4; 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}] (* A196259 *) y[n_] := u[[3 n - 1]]; Table[y[n], {n, 1, z7}] (* A196260 *) z[n_] := u[[3 n]]; Table[z[n], {n, 1, z7}] (* A196261 *) 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]] (* A196262 *) g = Table[y1[n], {n, 1, z9}]; y2 = Delete[g, Position[g, 0]] (* A196263 *) h = Table[z1[n], {n, 1, z9}]; z2 = Delete[h, Position[h, 0]] (* A196264 *)
Extensions
Corrected by Robert Israel, Dec 18 2024
Comments