Counting - discussion thread

[RobbieM]

1190 is a pronic number

Which means it's the product of two consecutive integers, I think - presumably 34 x 35.

And curiously, when you halve such a number, you end up with the sum of the series from 1 to the lowest of the two starting numbers.

e.g. 1+2+3+...+33+34=595 (half of 1190).

[The Orange One]

Curiously? It's just a fact of life, makes perfect sense.

[RobbieM]

Yes, sorry - a bad choice of word for my figure of speech (or maybe a curious one? )

[DrainBrain]

And curiously, when you halve such a number, you end up with the sum of the series from 1 to the lowest of the two starting numbers.

Pictorially:

Code: Select all

XXXXX        X  XXXX
XXXXX   ->   XX  XXX
XXXXX   ->   XXX  XX
XXXXX        XXXX  X

[RobbieM]

A wonderful work of art - thank you!

[GuyBarry]

Start with 1. Say what you see.

1
11
21
1211

(In case people haven't got it, that's "one 1" or 11, "two 1s" or 21, "one 2, one 1" or 1211 - so the next item is 111221, then 312211 and so on.)

When I was at university I went to a talk by John Conway, who introduced that sequence and first analysed it - it's known as the "look-and-say" sequence. There's an incredible theorem about it which says that every such sequence will eventually split up into a number of "elements", and by an amazing coincidence there are exactly 92 such elements - the same as the naturally occurring chemical elements!

[GuyBarry]

You can tell the QI Forum that a bunch of mis-matched tube challengers are ahead of them.

They've almost caught up now - 1207 against our 1220:

http://old.qi.com/talk/viewtopic.php?t=17100&start=1290

I no longer take part there, but it's got a bit sluggish here recently. I hope that some people here are interested in staying ahead.

[GuyBarry]

They're only seven behind now, and it looks practically certain that they'll overtake us. If they do, I'm afraid I'll have to go over and join them. I'm keen to submit some new entries and I can't wait for this forum to catch up.

[RobbieM]

I've got it moving again, slightly...

[GuyBarry]

Ah, that's the spirit! They're on 1218 now, I've just got ours up to 1223. Let's try to keep that competitive edge.

[GuyBarry]

They've finally pulled ahead. They're on 1224 now:

http://old.qi.com/talk/viewtopic.php?t= ... b3c650b87f

I've got a post ready to go on 1225. What do I do? Only my sense of loyalty makes me hesitate.

EDIT: Oh, someone's just posted 1225 over there. Guess I'll wait then. Come on - do you want to fall behind a bunch of QI-ers?

[GuyBarry]

OK, I've just posted a message over there saying I'm sticking with this team. We can do it...

[RobbieM]

Just caught up again...

[GuyBarry]

1227 QI Facts To Blow Your Socks Off

Wait, that's from QI people!

And they didn't even use it themselves!

Well done team - ahead by two again.

EDIT: make that four!

[GuyBarry]

1239 the number of the code used by the elf to lower the sleigh in santa clause the film.

Wow, Andi has taken part for the first time since about 110 (I think). Now I know what it takes to get Tube Challengers motivated!