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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.

%I A089489 #12 Feb 16 2025 08:32:51
%S A089489 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,
%T A089489 31,32,33,30,31,44,33,40,35,36,49,40,45,40,43,44,43,48,49,52,49,48,53,
%U A089489 74,51,56,57,58,59,58,61,68,63,64,61,64,65,80,71,66,71,80,95,70,71,84
%N 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.
%C A089489 a(n)^2 + n^2 = A068487(n).
%C A089489 From _Robert Israel_, Dec 11 2024: (Start)
%C A089489 a(n) is the least k > n such that k^2 + n^2 is prime.
%C A089489 a(n) = n + 1 for n in A027861. (End)
%H A089489 Robert Israel, <a href="/A089489/b089489.txt">Table of n, a(n) for n = 1..10000</a>
%H A089489 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%H A089489 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RightTriangle.html">Right Triangle</a>
%p A089489 f:= proc(n) local k;
%p A089489   for k from n+1 by 2 do
%p A089489     if isprime(k^2 + n^2) then return k fi
%p A089489   od
%p A089489 end proc:
%p A089489 map(f, [$1..100]); # _Robert Israel_, Dec 11 2024
%Y A089489 Cf. A027861, A068487.
%K A089489 nonn
%O A089489 1,1
%A A089489 _Reinhard Zumkeller_, Nov 04 2003