cp's OEIS Frontend

A342583 Numbers k such that prime(k) is the hypotenuse of a Pythagorean triple where one leg is also prime.

%I A342583 #35 Apr 04 2021 00:53:25
%S A342583 3,6,18,42,82,271,284,369,445,682,1069,1193,1900,2241,3894,6137,7108,
%T A342583 8164,9658,10126,12645,14842,14936,17913,18420,19480,23893,24605,
%U A342583 28959,32913,36279,40847,43936,44559,45500
%N A342583 Numbers k such that prime(k) is the hypotenuse of a Pythagorean triple where one leg is also prime.
%C A342583 In such a triangle, the leg that is not prime is always the largest one and is equal to prime(k)-1; these even legs are in A067755. E.g. for a(2) = 6, prime(6) = 13 and the corresponding Pythagorean triple is (5, 12, 13). - _Bernard Schott_, Apr 03 2021
%H A342583 Robert Israel, <a href="/A342583/b342583.txt">Table of n, a(n) for n = 1..1000</a>
%e A342583 a(1) = 3, since prime(3) = 5 is the hypotenuse of the triple (3,4,5).
%p A342583 R:= NULL: count:= 0:
%p A342583 p:= 2:
%p A342583 while count < 100 do
%p A342583   p:= nextprime(p); n:= (p-1)/2; q:= 2*n^2+2*n+1;
%p A342583   if isprime(q) then
%p A342583     count:= count+1; r:= numtheory:-pi(q); R:= R, r;
%p A342583   fi
%p A342583 od:
%p A342583 R; # _Robert Israel_, Mar 22 2021
%t A342583 PrimePi[Take[Cases[Import["https://oeis.org/A067756/b067756.txt","Table"],{_,_}][[All,2]],100]]
%Y A342583 Cf. A067756 (the hypotenuses).
%Y A342583 Cf. A009000, A046083, A046084, A067755.
%K A342583 nonn
%O A342583 1,1
%A A342583 _Ivan N. Ianakiev_, Mar 16 2021