A089489 Smallest k greater than n such that (k^2-n^2, 2*k*n, k^2+n^2) is a primitive Pythagorean triple and the corresponding right triangle has a prime hypotenuse.

2, 3, 8, 5, 6, 11, 8, 13, 10, 13, 14, 13, 20, 15, 22, 19, 18, 23, 20, 23, 26, 23, 30, 25, 26, 31, 32, 33, 30, 31, 44, 33, 40, 35, 36, 49, 40, 45, 40, 43, 44, 43, 48, 49, 52, 49, 48, 53, 74, 51, 56, 57, 58, 59, 58, 61, 68, 63, 64, 61, 64, 65, 80, 71, 66, 71, 80, 95, 70, 71, 84

Offset: 1

Author

Reinhard Zumkeller, Nov 04 2003

Keywords

• nonn

Comments

a(n)^2 + n^2 = A068487(n).

From Robert Israel, Dec 11 2024: (Start)

a(n) is the least k > n such that k^2 + n^2 is prime.

a(n) = n + 1 for n in A027861. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pythagorean Triple
• Eric Weisstein's World of Mathematics, Right Triangle

Crossrefs

Cf. A027861, A068487.

Programs

Maple

f:= proc(n) local k;
  for k from n+1 by 2 do
    if isprime(k^2 + n^2) then return k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 11 2024