A381336 a(n) is the smallest k > 0 for which a nondegenerate integer-sided triangle (k, k + n, c >= k + n) with an integer area exists.

3, 6, 9, 12, 12, 18, 5, 7, 4, 24, 14, 36, 15, 10, 36, 14, 7, 8, 6, 21, 8, 3, 12, 5, 10, 15, 12, 20, 46, 35, 9, 28, 20, 14, 25, 16, 15, 12, 22, 21, 19, 16, 12, 6, 20, 5, 4, 10, 11, 20, 21, 30, 96, 24, 13, 9, 18, 7, 25, 63, 21, 18, 22, 9, 35, 9, 25, 21, 36, 17, 13

Offset: 1

Author

Felix Huber, Mar 16 2025

Keywords

• nonn

Comments

Longest sides c are in A381337.

Examples

			a(5) = 12 because the nondegenerate integer-sided triangle (12, 12 + 5, 25 >= 12 + 5) has an integer area (90), and there is no smaller k > 0 than 12 that satisfies this condition.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Heron's Formula.

Crossrefs

Cf. A103974, A103975, A188158, A379830, A381337.

Programs

Maple

A381336:=proc(n)
    local k,c,s;
    for k do
        for c from k+n to 2*k+n-1 do
            s:=(n+2*k+c)/2;
            if issqr(s*(s-k)*(s-k-n)*(s-c)) then
                return k
            fi
        od
    od;
end proc;
seq(A381336(n),n=1..71);