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

3, 6, 18, 42, 82, 271, 284, 369, 445, 682, 1069, 1193, 1900, 2241, 3894, 6137, 7108, 8164, 9658, 10126, 12645, 14842, 14936, 17913, 18420, 19480, 23893, 24605, 28959, 32913, 36279, 40847, 43936, 44559, 45500

Offset: 1

Author

Ivan N. Ianakiev, Mar 16 2021

Keywords

• nonn

Comments

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

Examples

			a(1) = 3, since prime(3) = 5 is the hypotenuse of the triple (3,4,5).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067756 (the hypotenuses).

Cf. A009000, A046083, A046084, A067755.

Programs

Maple

R:= NULL: count:= 0:
p:= 2:
while count < 100 do
  p:= nextprime(p); n:= (p-1)/2; q:= 2*n^2+2*n+1;
  if isprime(q) then
    count:= count+1; r:= numtheory:-pi(q); R:= R, r;
  fi
od:
R; # Robert Israel, Mar 22 2021

Mathematica

PrimePi[Take[Cases[Import["https://oeis.org/A067756/b067756.txt","Table"],{,}][[All,2]],100]]