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

1,1

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A009003, A008846, A020882, A004613, A354381.

Sequence in context: A236849 A236834 A033902 * A009177 A118882 A085625

Adjacent sequences: A354376 A354377 A354378 * A354380 A354381 A354382

Keyword

nonn

Author

Lamine Ngom, May 24 2022

Status

approved