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

1,1

Comments

Longest sides c are in A381337.

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Heron's Formula.

Example

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.

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);

Crossrefs

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

Sequence in context: A122809 A066662 A329517 * A297567 A285402 A153403

Adjacent sequences: A381333 A381334 A381335 * A381337 A381338 A381339

Keyword

nonn

Author

Felix Huber, Mar 16 2025

Status

approved