Counting - discussion thread

[RobbieM]

I think we got away with it...

[tubeguru]

Whatever.

[tractakid]

678*4=/=5678

[tubeguru]

Whatever.

[GuyBarry]

I think tubeguru was perfectly OK with that one. He said it's three-quarters of the title, not three-quarters of the number.

Or perhaps there's some obscure Steps single called "904" that I'm unaware of

[tubeguru]

Yeah, I'm saving that one for when we get to 904.

[GuyBarry]

The 684th Fibonacci number is divisible by 684.

Feel free to tell us what it actually is ...

It appears to be:

39633363350150665433335490556348985189574179795039333969368895830540407820581547578204201061028307874718885735558275776690548029037838240694288

I haven't checked for divisibility by 684 though.

EDIT: sorry, this formatting has cut the last three digits off the number. It actually ends ...694288.

EDIT[2]: this site gives prime factorizations of all the Fibonacci numbers up to the 1000th. The factorization of the 684th number begins 2^4 * 3^3 * 17 * 19^2..., and 684 = 2^2 * 3^2 * 19, so DrainBrain is definitely right. No idea where he got the information from though!

[RobbieM]

Wow. Have you memorised it? I ran out of memorising Fibonnaci numbers after 1,1,2,3,5,8,13,21,34,55,89 ... that's it; I have to add them in my head now.

[GuyBarry]

Wow. Have you memorised it?

No, of course not! You can get the values of Fibonacci numbers from the Fibonacci calculator.

[RobbieM]

Wow. Have you memorised it?

No, of course not! You can get the values of Fibonacci numbers from the Fibonacci calculator.

And what you may not know is, that I was once a lodger in the house of Dr R.Knott in1994/5!

[GuyBarry]

690 - the last three digits of the STD code for Betws-y-Coed. That's a nice sounding place. I guess the digits may represent NW - North Wales, though I haven't checked.

Not according to the list I cited earlier, which gives "coNWy valley" - weird one though!

[GuyBarry]

I'm not turning the thread into a list of road numbers!

Having said that, I'll be impressed if you know where the A700 is off the top of your head. I have walked its entire length, which is nothing like as impressive as it sounds...

[DrainBrain]

Apologies for not providing a link re the 684th Fibonacci number. The source was OEIS which includes a sequence of nth Fibonacci numbers that are divisible by n: http://oeis.org/A023172

Because the number is over 140 decimal digits I didn't bother posting it.

[GuyBarry]

Ah yes, the Online Encyclopedia of Integer Sequences - ultimate bible for anyone interested in the properties of the natural numbers. I came across it a few years ago and was amazed to discover that such a thing existed. A couple of years ago the BBC programme QI said that 12407 was the "smallest uninteresting number" because at the time it was the smallest number that didn't appear in the OEIS. (I'm not sure what it is now - it was 13794 for a while, but I think that appears now.) Of course, the smallest uninteresting number is by definition interesting, giving rise to the well-known interesting number paradox.

Which means that the counting game should keep going for quite a while yet

[RobbieM]

Ah yes, how long do you think it'll take us to get to 12,407?