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A381337 a(n) is the smallest c >= A381336(n) + n for which a nondegenerate integer-sided triangle (A381336(n), A381336(n) + n, c) with an integer area exists.

%I A381337 #5 Mar 25 2025 23:53:58
%S A381337 5,10,15,20,25,30,13,20,15,50,25,60,41,26,75,40,25,30,29,50,35,26,37,
%T A381337 30,39,52,45,52,109,82,41,80,55,50,65,60,61,58,61,68,73,70,65,52,75,
%U A381337 52,53,60,61,78,75,104,203,90,75,70,87,68,101,150,89,82,91,80,117
%N A381337 a(n) is the smallest c >= A381336(n) + n for which a nondegenerate integer-sided triangle (A381336(n), A381336(n) + n, c) with an integer area exists.
%H A381337 Felix Huber, <a href="/A381337/b381337.txt">Table of n, a(n) for n = 1..10000</a>
%e A381337 a(5) = 25 because A381336(n) = 12 and the nondegenerate integer-sided triangle (12, 12 + 5, 25 >= 12 + 5) has an integer area (90), and there is no smaller c > 12 + 5 than 25 that satisfies this condition.
%p A381337 A381337:=proc(n)
%p A381337     local k,c,s;
%p A381337     for k do
%p A381337         for c from k+n to 2*k+n-1 do
%p A381337             s:=(n+2*k+c)/2;
%p A381337             if issqr(s*(s-k)*(s-k-n)*(s-c)) then
%p A381337                 return c
%p A381337             fi
%p A381337         od
%p A381337     od;
%p A381337 end proc;
%p A381337 seq(A381337(n),n=1..65);
%Y A381337 Cf. A381336.
%K A381337 nonn
%O A381337 1,1
%A A381337 _Felix Huber_, Mar 18 2025