On 02/02/2020 18:56, Keith F. Lynch wrote:
There have been no posts in response to either of my mystery tables for over a week. Is anyone still working on them, or shall I reveal what they are tables of? Here they are again:
1 2 3 4 5 6 7 8 1: all 2: -inf +inf 3: -inf 1.000000 +inf 4: -inf 0.000000 2.261406 +inf 5: -inf -0.349081 1.000000 3.074601 +inf 6: -inf -0.523305 0.523305 1.564328 3.795684 +inf 7: -inf -0.626499 0.268479 1.000000 2.000000 4.495526 +inf 8: -inf -0.694242 0.109189 0.694242 1.350067 2.385122 5.190739 +inf 9: -inf -0.741892 0.000000 0.500000 1.000000 1.643796 2.748616 5.884929 10: -inf -0.777116 -0.079600 0.364842 0.777116 1.249756 1.908997 3.102748 11: -inf -0.804148 -0.140255 0.265003 0.621297 1.000000 1.469217 2.158924 12: -inf -0.825509 -0.188046 0.188046 0.505587 0.825509 1.192579 1.671024 13: -inf -0.842792 -0.226700 0.126799 0.415933 0.695796 1.000000 1.366735 14: -inf -0.857046 -0.258628 0.076822 0.344232 0.595108 0.857046 1.155985 15: -inf -0.868994 -0.285461 0.035215 0.285461 0.514414 0.746112 1.000000 16: -inf -0.879146 -0.308343 0.000000 0.236333 0.448129 0.657173 0.879146 I have been thinking half-heartedly (and apparently half-brainedly) about this one from time to time ... and in the process of writing down my incoherent thoughts I realise that I have solved it.
... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... ... spoiler space ... The value in row m, column n is the k such that m^k = 2n^k-1. For the (1,1) entry any k will do, hence the slightly curious "all" in that spot. (I haven't looked at the second table.) -- g