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I hope this doesn’t sound like a message on the other site! I found the gridfill easier than usual, with no calculator needed, but the endgame certainly called for a calculator. This gave me mixed feelings. On the one hand, it seemed to have no connection at all with crossword solving. On the other hand, it revealed an extraordinary and beautiful property shared by these sets of numbers.

So the reason for posting this message is to encourage forumites who might be deterred by numerical puzzles to give it a go. And perhaps I may be forgiven if I slip in an unasked-for caveat: don’t overlook trivial values of N.

Filled grid and found the common property without too much grief then came to a complete halt. I got to N=104 before Excel gave up on me so I assume I am doing something wrong.

I agree, Rad. This was very straightforward, although not all that rewarding since the denouement was irrelevant to the solving. It left me a bit deflated if truth be told; the previous Listener numerical had been great fun and extremely clever, I thought. Ho hum.

Tatters either you've done something wrong or I have, as I get N is true for a small number of powers.

Agreed, Gitto. I was wondering if I’d gone wrong, but will check again later.

Tatters, just a thought, but N is for consecutive integers only.

All sorted chaps but thanks for suggestions. Just a dodgy formula that was looking for the first non-zero value of x-x say rather than x-y. No real surprise that I couldn't find the solution.

It's a good job you stopped at 104, otherwise you will still be going!! I often find that I make elementary errors with math puzzles which means I only solve them at attempt 3+. Fortunately I didn't slip up this time!

tatters, not only is B (for the consecutive range from A to B) much smaller than 104, but I am pretty sure that the property is not true for ANY integer greater than B

You're all well ahead of me. I gave up last night, after deciding that 19d had to begin with 2, 7 or 8, but that 18ac couldn't end in any of those digits. Impasse! Suggestions as to where I might have gone wrong would be welcome.