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

1,1

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

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

Crossrefs

Cf. A027861, A068487.

Sequence in context: A308360 A324364 A265344 * A284047 A265343 A347193

Adjacent sequences: A089486 A089487 A089488 * A089490 A089491 A089492

Keyword

nonn

Author

Reinhard Zumkeller, Nov 04 2003

Status

approved