A354379 Hypotenuses of Pythagorean triangles whose legs are also hypotenuse numbers (A009003).
25, 50, 65, 75, 85, 89, 100, 109, 125, 130, 145, 149, 150, 169, 170, 173, 175, 178, 185, 195, 200, 205, 218, 221, 225, 229, 233, 250, 255, 260, 265, 267, 275, 289, 290, 293, 298, 300, 305, 313, 325, 327, 338, 340, 346, 349, 350, 353, 356, 365, 370, 375, 377, 390, 400
Offset: 1
Keywords
Examples
25 is in sequence since each member of the Pythagorean triple (15, 20, 25) belongs to A009003. The Pythagorean triple (39, 80, 89) has all its terms in A009003. Hence 89 is in sequence.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
ishyp:= proc(n) local s; ormap(s -> s mod 4 = 1, numtheory:-factorset(n)) end proc: filter:= proc(n) local s; ormap(s -> ishyp(subs(s,x)) and ishyp(subs(s,y)), [isolve(x^2+y^2=n^2)]) end proc: select(filter, [$1..1000]); # Robert Israel, Jan 10 2023
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Mathematica
ishyp[n_] := AnyTrue[FactorInteger[n][[All, 1]], Mod[#, 4] == 1&]; filter[n_] := AnyTrue[Solve[x^2 + y^2 == n^2, Integers], ishyp[x /. #] && ishyp[y /. #]&]; Select[Range[400], filter] (* Jean-François Alcover, May 11 2023, after Robert Israel *)
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