A354379 - OEIS

%I #15 May 11 2023 09:11:19

%S 25,50,65,75,85,89,100,109,125,130,145,149,150,169,170,173,175,178,

%T 185,195,200,205,218,221,225,229,233,250,255,260,265,267,275,289,290,

%U 293,298,300,305,313,325,327,338,340,346,349,350,353,356,365,370,375,377,390,400

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

%C If m is in sequence, so is any multiple of m. Primitive elements (terms which are not divisible by any previous term) are A354381.

%H Robert Israel, <a href="/A354379/b354379.txt">Table of n, a(n) for n = 1..10000</a>

%e 25 is in sequence since each member of the Pythagorean triple (15, 20, 25) belongs to A009003.

%e The Pythagorean triple (39, 80, 89) has all its terms in A009003. Hence 89 is in sequence.

%p ishyp:= proc(n) local s; ormap(s -> s mod 4 = 1, numtheory:-factorset(n)) end proc:

%p filter:= proc(n) local s;

%p   ormap(s -> ishyp(subs(s,x)) and ishyp(subs(s,y)), [isolve(x^2+y^2=n^2)])

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jan 10 2023

%t ishyp[n_] := AnyTrue[FactorInteger[n][[All, 1]], Mod[#, 4] == 1&];

%t filter[n_] := AnyTrue[Solve[x^2 + y^2 == n^2, Integers], ishyp[x /. #] && ishyp[y /. #]&];

%t Select[Range[400], filter] (* _Jean-François Alcover_, May 11 2023, after _Robert Israel_ *)

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

%K nonn

%O 1,1

%A _Lamine Ngom_, May 24 2022