Counting - discussion thread

[GuyBarry]

I think it was the former A604!

Correct! Probably my favourite non-existent road of all

[GuyBarry]

The Scottish village of Fort Augustus is where my parents live. It is beautifully set on the Caledonian Canal, at the very bottom end of Loch Ness. Sea-going yachts emerge from the top of the flight of five locks to continue their journey down towards Fort William. A wonderful place to go for holidays. (And still part of the UK, as I'm writing....)

The village also has its own STD code, which ends 1320.

With a population of 646 (according to Wikipedia)? It needs an entire range of 800,000 numbers? (Six digits long, with a first digit other than 0 or 1.)

[RobbieM]

I think they had STD codes to spare at the time. And actually, it does pick up some of the surrounding area, but Fort Augustus is the centre of it. So maybe 'its own STD code' was misleading; sorry!

[GuyBarry]

It can still only be a few thousand people though.

It annoys me that we were told back in the 1990s that we all needed an extra digit in our phone codes because the country was supposedly "running out of numbers", yet there are areas like Fort Augustus that are still vastly under-capacity.

[RobbieM]

If only they'd've known when they allocated STD codes just how much communications would develop over the following decades. I bet they never thought London would run out of numbers when they gave it '01'.

[DrainBrain]

1369 is a perfect square (= 37^2), which as written in base 10 is made up of three other perfect squares (1, 36, 9).

Also, the digits increase strictly from left to right (i.e. they don't get smaller, and no two digits are the same). I think it may be the highest perfect square with this property, but I haven't been able to verify it yet. I certainly haven't found a higher one on this list, but feel free to prove me wrong!

Guessing you scanned the list quickly because you missed some higher ones. Here's the full list:

0, 1, 4, 9, 16, 25, 36, 49, 169, 256, 289, 1369, 13456, 13689, 134689

I found these myself, but then searched for this sequence at OEIS and found http://oeis.org/A122683.

If you allow repeating digits you can get up to 16667^2 = 277788889

[GuyBarry]

Ah, thanks very much. Good old OEIS - the answer's always there somewhere!

[DrainBrain]

If you allow repeating digits you can get up to 16667^2 = 277788889

Actually, I stopped my program too soon and there are infinite families of squares with non-decreasing digits:

167^2 = 27889
1667^2 = 2778889
16667^2 = 277788889
etc.

With similar patterns for:

334, 3334, 33334, ...
335, 3335, 33335, ...

and

(3)(6)7, where (x) means any number, possibly zero, of digit x.

Also a few one-offs: 3383, 4833, 105462, 125167. Maybe more.

[The Orange One]

In fact horses are so fast, they often race each other

I think this is one of the funniest things I've read on the forum. Maybe I've just got a dodgy sense of humour, though.

[RobbieM]

Maybe I've just got a dodgy sense of humour, though.

You and me both. Next time I'll be talking about slugs racing each other...

[GuyBarry]

Congratulations to DrainBrain on getting the current Counting thread up to 1000 posts. (Since the first counting post in the thread was 433, the 1000th really ought to be at 1432; but a few non-counting posts have sneaked in over the course of the thread.)

[GuyBarry]

1395 – vampire number, member of the Mian–Chowla sequence

My curiosity was piqued by this one. According to Wikipedia, "a vampire number (or true vampire number) is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains precisely all the digits from x and from y, in any order, counting multiplicity. x and y are called the fangs". So 1395 is a vampire number because it equals 15 x 93.

http://en.wikipedia.org/wiki/Vampire_number

The Mian-Chowla sequence is a bit more complicated to explain, but it can be found here:

http://en.wikipedia.org/wiki/Mian%E2%80 ... a_sequence

[GuyBarry]

QI have got to 1400, which means they're only one behind us now. Can we keep our lead?

http://old.qi.com/talk/viewtopic.php?t=17100&start=1500

[RobbieM]

We'll try! Now I've finished accompanying a big performance of Fauré's Requiem, I'll pop into the forum a bit more.

[The Orange One]

Oh well, here we go! Keep trying...