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

%I A354379 #15 May 11 2023 09:11:19
%S A354379 25,50,65,75,85,89,100,109,125,130,145,149,150,169,170,173,175,178,
%T A354379 185,195,200,205,218,221,225,229,233,250,255,260,265,267,275,289,290,
%U A354379 293,298,300,305,313,325,327,338,340,346,349,350,353,356,365,370,375,377,390,400
%N A354379 Hypotenuses of Pythagorean triangles whose legs are also hypotenuse numbers (A009003).
%C A354379 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 A354379 Robert Israel, <a href="/A354379/b354379.txt">Table of n, a(n) for n = 1..10000</a>
%e A354379 25 is in sequence since each member of the Pythagorean triple (15, 20, 25) belongs to A009003.
%e A354379 The Pythagorean triple (39, 80, 89) has all its terms in A009003. Hence 89 is in sequence.
%p A354379 ishyp:= proc(n) local s; ormap(s -> s mod 4 = 1, numtheory:-factorset(n)) end proc:
%p A354379 filter:= proc(n) local s;
%p A354379   ormap(s -> ishyp(subs(s,x)) and ishyp(subs(s,y)), [isolve(x^2+y^2=n^2)])
%p A354379 end proc:
%p A354379 select(filter, [$1..1000]); # _Robert Israel_, Jan 10 2023
%t A354379 ishyp[n_] := AnyTrue[FactorInteger[n][[All, 1]], Mod[#, 4] == 1&];
%t A354379 filter[n_] := AnyTrue[Solve[x^2 + y^2 == n^2, Integers], ishyp[x /. #] && ishyp[y /. #]&];
%t A354379 Select[Range[400], filter] (* _Jean-François Alcover_, May 11 2023, after _Robert Israel_ *)
%Y A354379 Cf. A009003, A008846, A020882, A004613, A354381.
%K A354379 nonn
%O A354379 1,1
%A A354379 _Lamine Ngom_, May 24 2022