cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A354379 Hypotenuses of Pythagorean triangles whose legs are also hypotenuse numbers (A009003).

Original entry on oeis.org

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

Views

Author

Lamine Ngom, May 24 2022

Keywords

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.

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.
		

Crossrefs

Programs

  • 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 *)
Showing 1-1 of 1 results.