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A354379
Hypotenuses of Pythagorean triangles whose legs are also hypotenuse numbers (A009003).
2
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
1,1
COMMENTS
If m is in sequence, so is any multiple of m. Primitive elements (terms which are not divisible by any previous term) are A354381.
LINKS
EXAMPLE
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.
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Lamine Ngom, May 24 2022
STATUS
approved