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

1,1

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

Links

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

Example

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

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]]

Crossrefs

Cf. A067756 (the hypotenuses).

Cf. A009000, A046083, A046084, A067755.

Sequence in context: A356766 A181037 A222856 * A007990 A197050 A354387

Adjacent sequences: A342580 A342581 A342582 * A342584 A342585 A342586

Keyword

nonn

Author

Ivan N. Ianakiev, Mar 16 2021

Status

approved