Twitter to the rescue
July 15, 2009I asked my followers on twitter to help me in my search to understand what I’d called Saturday numbers better (I now have a proper name for them. More on that later).
@paulhertz replied an gave me some helpful links.
Firstly – a name
What I’ve been calling a Saturday number in base b is a b-Niven repunit.
How cool does that sound?
I didn’t spend the weekend messing about with some problem I heard on a podcast. I was investigating b-Niven repunits. I now what that means, but it still sounds awfully impressive.
A Niven number is one that is divisible by the sum of it’s digits (so 18 is divisible by 1+9 so is a Niven number, 19 isn’t divisible by 1+9 so it isn’t one).(Read more on Wikipedia).
A repunit has repeated digits. (Read more on Wikipedia).
That’s why my Saturday numbers are called b-Niven repunits (for base b).
Proper maths
Because @paulhertz also sent me some references and I’ve been following them up:
..which appears to be a bit of a dead end. I might have been able to track it down back when I was at University. But you might be surprised to know that I don’t have a 1989 copy of Fibonacci Quarterly on my shelves.
And this:
http://www.maths.tcd.ie/pub/ims/bull59/R5901.pdf
That’s more like it!
I’m going to look forward to reading this one.
Fibonacci Quarterly doesn’t seem to be that widely available. At neither university in Nottingham and I can’t find it electronically. In fact the only copies I can find reference to are at:
British Library
& Universities of:
Leicester
Reading
St Andrews
Swansea
if you ever happen to be near any of those!
http://suncat.edina.ac.uk/F?func=find-b&request=0015-0517&find_code=ISSN
I’m in London on business next week – so the British Library looks like my best bet.
Adam, Is this a potential research area? Other than a mathemeatical research interest, are there any real world ramifications for repunits?
Firstly, I don’t think there’s anything new in this. So, no, I don’t think there’s any real research here.
Secondly, It’s wrong to say that any pure maths is pointless. Maths has a habit of popping up in the most unusual places.
But, if there were such a thing as pointless maths then this would be it!
Well you could always setup a graphics algo such that, for every mod=0, bring it back to [x-a], [y-b] coordinate and see what picture you would get..
We may just get interesting results..
I’d already generated a picture http://adamjtp.files.wordpress.com/2009/07/out.png?w=120&h=1020 – but it doesn’t show anything interesting. Shame really. It’s nice when there’s a pretty pattern hiding in there.
Adam!
Dang!! there goes the one attempt at fame and glory, the allelujah of patterns, a pretty fractal, no one discovered before..
Sorry for not responding right away, been busy.. The pattern looks very close to a binary 10 sequence, so I am thinking visual representation of a cipher?