Is there a number f(n) such that 1/f(n) yields all n-digit numbers, and is there a formula f to generate them?
Fun with math: Dividing one by 998001 yields a surprising result
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Re: Fun with math: Dividing one by 998001 yields a surprising result
#12This can be seen in python with (I had to dig into the docs for this, so here are the fruits of my labor :) ) import decimal decimal.getcontext().prec=1000 dec = decimal.Decimal(1)/decimal.Decimal(998001) #now doctor it up to see the numbers strdec = str(dec)[2:] #chop off the '0.' nums = zip(strdec[::3],strdec[1::3],strdec[2::3]) print nums
You've got an extra ) on the 'nums = .....'
Re: Fun with math: Dividing one by 998001 yields a surprising result
#13This can be seen in python with (I had to dig into the docs for this, so here are the fruits of my labor :) ) import decimal decimal.getcontext().prec=1000 dec = decimal.Decimal(1)/decimal.Decimal(998001) #now doctor it up to see the numbers strdec = str(dec)[2:] #chop off the '0.' nums = zip(strdec[::3],strdec[1::3],strdec[2::3]) print nums
I don't have a python shell available... what happens after 999?
It repeats.
EDIT: Um... I answered the good man's question. Could someone explain why this correct answer was voted down so I may improve it? I recognize that it is short, but that's really all there is too it. It's a decimal expansion, not a border collie.
Re: Fun with math: Dividing one by 998001 yields a surprising result
#14You can see it at Wolfram Alpha http://www.wolframalpha.com/input/?i=1%2F998001
Re: Fun with math: Dividing one by 998001 yields a surprising result
#15[deleted]
Re: Fun with math: Dividing one by 998001 yields a surprising result
#16This can be seen in python with (I had to dig into the docs for this, so here are the fruits of my labor :) ) import decimal decimal.getcontext().prec=1000 dec = decimal.Decimal(1)/decimal.Decimal(998001) #now doctor it up to see the numbers strdec = str(dec)[2:] #chop off the '0.' nums = zip(strdec[::3],strdec[1::3],strdec[2::3]) print nums
The period is 2997, so set precision to 2997 if you want to see the repeat. Also, "998" doesn't appear 'in sequence' (it obviously appears as 97[9 98]0 981).
Edit: That's strange, about 998 being absent. What follows is definitely nonsense:
Don't really have time to think about this, but you can sort of generate the sum (ie by looking at the pattern) with
(1/1000) * sum i * 1000^-i , i = 0 to infinity
You could try and do a sum of a sum of geometric series and make it work
http://www.wolframalpha.com/input/?i=sum+i+*+1000%5E-i%2C+i%...
(998001 / 2997 = 3)
Re: Fun with math: Dividing one by 998001 yields a surprising result
#17The source with real (readable) text, without annoying animation: http://www.futilitycloset.com/2012/01/08/math-notes-76/
So we're missing 998 here in actuality ?
Re: Fun with math: Dividing one by 998001 yields a surprising result
#18Is there a number f(n) such that 1/f(n) yields all n-digit numbers, and is there a formula f to generate them?
You may play with the Champernowne constant :
Re: Fun with math: Dividing one by 998001 yields a surprising result
#19Thanks for posting. I'm trying to keep a collection of these type of things so that when she's ready, it'll be another tool to get/keep my daughter excited about math.
Re: Fun with math: Dividing one by 998001 yields a surprising result
#20I was searching for some iOS documentation and found this and it's totally ruined my productivity! Can anyone explain why it repeats in this way, or link to a place that has an explanation?
For x < 1, 1 + 2x + 3x^2 + 4x^3 + ... converges to 1/(1-x)^2. When x = 0.001, you get 1/.999^2 = 1000000/998001 = 1.002003004005...