Number Theory

 Posted by on July 3, 2008  Add comments
Jul 032008

Do you know the number 142857?

No. I didn’t think so, and why the hell should you?

Normal people are out enjoying themselves, getting drunk, singing songs, having fun, talking small-talk while fuckers like me are finding out about 142857.  What a sad bastard.  Even my beloved Bullet, who by the way is sixteen today and no longer a child, looks at me in pity and says

You know what, Bock, you are indeed a nerd and a geek.

I’m not a fucking geek, I bark, and punch him in his expensive orthodontised teeth.

All right then, he mumbles through globbing blood-dribbles.  A nerd.

Happy birthday, Bullet.  (Bullet is out of the country at the moment on a heavily subsidised foreign holiday, the bastard.)

Where was I?  Oh yes: 142857.

Did you ever come across Ramanujan? 

Well, Srinivasa Ramanujan was a great Indian mathematician, who went to Britain in 1914 at the age of 27 to research mathematics at Cambridge under GH Hardy.  He was a natural genius but a rather intense young fellow.  He was also unwell with a curable, but undiagnosed, liver disease and he found life in wartime England difficult for a vegetarian.  He didn’t last long, and by 1920 poor Ramanujan was dead, at the age of 32, but by then he’d produced thousands of mathematical conjectures that gave rise to an academic industry that spawned thousands of PhDs.   Good old Ramanujan.

Just before his final return to India, when Ramanujan was very ill, Hardy called to see him.  They struggled for conversation until Hardy, desperate for something to talk about, made a chance comment about his taxi’s number.

I say, Ramanujan, old boy.  That taxi had the most uninteresting number I’ve ever come across.

Ramanujan, close to death, sat up in his bed.  Really?  What was it?

Oh, I believe it was 1729.

Ramanujan forgot his fatal illness.  Oh, no no no!!  That is a most interesting number.  1729 is the smallest number that can be expressed as the sum of two cubes in two different ways.

Now, I don’t know about you, but I find that level of engagement disturbing.  I do really. Get a grip, Ramanujan.  Get a life!

Where was I?

Oh yeah.  142857.

Well, you see, the strange thing about 142857 is that if you multiply it by 2, you get 285714.

So what?  Well, if you look at it closely, you’ll notice that the answer is the same numbers in the same order, but moved along a little bit, but that’s not the only strange thing.

If you multiply it by 3, you’ll see that the result is 428571, which is also the same numbers in the same order.  And if you do the same with 4, 5 and 6, you’ll observe exactly the same thing.

How fucking strange.

I invite you to check this, and then to multiply it by 7.

Get a grip, Bock.  Get a fucking life!


Mathematically-inclined smart bastards need not necessarily feel the need to make snide comments about this.

  23 Responses to “Number Theory”

Comments (23)

    Wouldn’t a good knock of Guiness cure you of this?

    Just wondering.


    I am not a mathametically smart bastard but I do like these things that pop up in number theory – not sure why, just do. The easy ones, like all the multiples of 9 adding up to 9, e.g., 1+8, 2+7, 3+6 etc. are fascinating but for very superficial reasons – they just are!

    I also wonder at the way some people’s brains are wired and the inate ability to look at numbers and immediately relate them. One of the best books I read – The man who loved only numbers, by Paul Hoffman – is about Paul Erdos, a travelling mathematician and a giant in this area (number theory). This guy was multiplying telephone numbers in his head at the age of four – jaysus!


    Nice one Bock, I’m about as mathematically talented as burnt toast but I was given a book for Christmas last year about prime numbers:

    Well worth a read, there’s a whole section on your friend, Ramanujan and much more all written in language that burnt toast can understand!!


    Actually, that’s pretty cool!


    Go on the Bullet, is he filing copy from far off subsidised climes?

    It’s best if I stay clear of the number thing.


    And your point is. There has to be a fucking point. Your man Ramanujan, great crack at parties I’d say, great man for the jokes and the girls. No chance Bock and what’s more he’d never go to Thomand Park even if he had a Jesus Christ ticket for the All Blacks. The point Bock, please.


    Mmmm I like it.
    No good at numbers myself, but I admire this in others – kind of!
    Conan, do tell, why is it best you say nowt?
    Are you super good at numbers?
    Super bad?


    Mairéad, my brain’s bad enough with words. If I start on the numbers my brain starts playing with them in a weird multi-dimensional symbolic way – to no great mathematical effect, let me add. Same reason I’d never take hallucinogens.


    actually, I /did/ recognise that number.

    when I was a kid, I was told that a good approximation of pi is 22/7 – that’s 3.142857142857…

    so another interesting thing there is that if you take the string of numbers, repeat it over and over, and stick a ‘3.’ in front, you get 22/7.


    OP: Yes, it would, and it will. Thank you for the suggestion.

    GOM: That sounds like an interesting read. I’ll watch out for it.

    Swiss Job: Another interesting link, for which I thank you.

    Darren: Yes indeed it is.

    Conan: Is that some sort of synaesthesia?

    Sniffle: Sometimes there’s no point. Sometimes it’s just aimless rambling.

    Mairéad: We’ll get to the truth about Conan yet.

    Kae: Hello there and welcome. You’re right. It’s the recurring part of 1/7


    I like that, a number with character and a distinct characteristic, we need more of that, its whats lacking in numbers these days, in my day every number had character, being a patriot my favourite number would have to be tirty tree and a turd, now thats a real honest to goodness irish to its roots number, a fighting number, the kind of number that knows when its up and people got it.


    Sneaky numbers with their Goddammed hidden codes and patterns! I don’t trust them one little bit.


    I wonder if 1729 is a Keith number?

    Let me explain:

    A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the first n terms taken as the decimal digits of the number N, then N itself occurs as a term in the sequence.

    For example, 197 is a Keith number since it generates the sequence 1, 9, 7, 1+9+7==17, 9+7+17==33, 7+17+33==57, 17+33+57==107, 33+57+107==197, … (Keith).

    Keith numbers are also called repfigit (repetitive fibonacci-like digit) numbers.

    There is no known general technique for finding Keith numbers except by exhaustive search.

    Keith numbers are much rarer than the primes, with only 84 Keith numbers with <26 digits.

    I presumed they were called Keith numbers after Keith Richards but no – they are named after Mike Keith.

    Mike Keith is a mathematician who published a paper on these numbers titled “Repfigit Numbers” in a 1987 issue of ( I kid you not) The Journal of Recreational Mathematics.

    There was a possibility that we could have been calling them Mike Numbers or (heaven forbid) Mick Numbers but thankfully not!


    It wouldn’t take long to check that, except I’m going for a pint now. Let me know how you get on.


    Just the one PInt, Bock?


    That is sooo cool bock. I LOVE numbers!!! never heard of that one.

    I’ve a 16 year old too. Now there’s a number I could do something with only I cant say it here!!


    No. A transcendental number of them.


    Bock – totally tangential post here, but you have reminded me of a book which I think you might enjoy. Its called Cryptonomicon, by Neal Stephenson. Stephenson is a bit of a genius who manages to write novels involving history, science, maths, and various other fileds – you name it really, and make them fascinating. Cryptonomicon involves a mathematical genius who is recruited to in the enigma project cracking Nazi codes, ends up on wild and wonderful adventures. Sorry, I’m no reviewer, so cant describe it very well, but I think most enquiring minds, especially of a technical bent, would enjoy it.


    ahem… the Hollies, a band, from the sixties and on, had, in the eighties, if one is not mistaken, an album called, wait for it, 5317704. Yeah you need a seventies calculator to get it. (sorry, just in from the watering hole and this is about as numerical as I get this time of an eve’).


    335 1


    “Is that some sort of synaesthesia?”
    Probably not as pronounced as that.


    710 77345 (royalties)


    I can actually relate to all this stuff!
    Do I need to worry?

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