My quick search suggests that k = T(n)/2 seems to be an upper bound. It looks like this boundary will be reached when m = k+1, for example, (n,k,m) = (7,27,28), (16,135,136), and (31,495,496). Kerry On Wed, Feb 19, 2020 at 10:46 AM Allan Wechsler <acwacw@gmail.com> wrote:
I think that k = T(n) - 1 is an upper bound. T(k) makes a huge triangle; all the elements of the T(n) triangle can be thinly plated onto the side of the big one as a single additional row, producing T(k+1), so m = k+1. I think m-k would also make an interesting sequence.
On Wed, Feb 19, 2020 at 12:35 PM Neil Sloane <njasloane@gmail.com> wrote:
Let T(i) = i(i+1)/2. Given n, let k be smallest number such that T(n) + T(k) = T(m) for some m. The k and m values are in A082183 and A082184. It must be classical that k and m always exist. - can someone supply a reference or a proof?
The graph of the k values is quite irregular. Is there an upper bound? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun