[seqfan] Re: Pi in Pi (with a "divide sign")

[Eric Angelini]

> more detail to A048940

... Indeed, yes - selfreference is everywhere!
;-D
É.


-----Message d'origine-----
De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de Charles Greathouse
Envoyé : jeudi 17 juillet 2014 15:58
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Pi in Pi (with a "divide sign")

This is cute, Eric. I like that the start of the second block of successive improvements is a supersequence of the location of the largest block of consecutive 9s seen so far -- sort of adds more detail to A048940.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Thu, Jul 17, 2014 at 8:15 AM, M. F. Hasler <oeis at hasler.fr> wrote:

> On Thu, Jul 17, 2014 at 1:33 PM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
> > Merci Maximilian -- yes, the 999... strings are a clue, but do they 
> > beat strings like 99899.. or 99998899, etc. ?
>
> yes, of course; e.g. if the denominator starts 998... then the result 
> will be off by something between 1/1000 .. 2/1000 (depending on the 
> next digit).
> At first sight, a less trivial question would result if the roles of 
> numerator or denominator would be exchanged, but a second thought 
> shows that this would only change the digits one has to look for, 
> which would be 98696044010..., then.
> (eg, cutting 2 chunks of 80 decimals yields 98628.../314159.... = 
> 3.139..., but one has to go a lot further to get a significant
> improvement.)
>
> M.
> > -----Message d'origine-----
> > De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de M. F.
> Hasler
> > Envoyé : jeudi 17 juillet 2014 13:14 À : Sequence Fanatics 
> > Discussion list Objet : [seqfan] Re: Pi in Pi (with a "divide sign")
> >
> > Hello Eric,
> > to beat this, it is sufficient to choose the start of an arbitrarily
> long string of 99...99 or 100..00, and it is most probable that there 
> are infinitely many such.
> >
> > For example, the string 99999 occurs at position 762. (This string
> occurs 1956 times in the first 200M digits of Pi.
> > counting from the first digit after the decimal point: The 3. is not
> counted.) The string 9999999 occurs at position 1722776. This string 
> occurs
> 18 times in the first 200M digits of Pi.
> > The string 99999999 occurs at position 66780105. This string occurs 
> > 1
> times in the first 200M digits of Pi.
> >
> > So, if you cut after the 762 decimals and make the second cut 
> > (discard
> the rest) after the 1524-th decimal digit, then the ratio equals Pi to 
> approx. 6 digits :
> > 31415926..0721134/9999998372....  = pi + 5.747 x 10^(-7)
> >
> > Nice summer vacation to all SeqFans, Maximilian
> >
> > On Thu, Jul 17, 2014 at 12:36 PM, Eric Angelini 
> > <Eric.Angelini at kntv.be>
> wrote:
> >>
> >> Hello SeqFans,
> >>
> >>
> >>
> >> Step 1 - I concatenate the first 173 consecutive digits of Pi:
> >>
> >> 3141592653589793238462643383279502884197169399375105820974944592307
> >> 816
> >> 4062862089986280348253421170679821480865132823066470938446095505822
> >> 317
> >> 25359408128481117450284102701938
> >>
> >>
> >>
> >> Step 2 - I insert the divide sign "/" somewhere to produce a fraction:
> >>
> >> 3141592653589793238462643383279502884197169399375105820974944592307
> >> 816
> >> 406286208/998628034825342117067982148086513282306647093844609550582
> >> 231
> >> 725359408128481117450284102701938
> >>
> >>
> >>
> >> Step 3 - The fraction = 3.1459...
> >>
> >>
> >>
> >> Can you beat that? (this is, get closer to Pi)?
> >>
> >>
> >>
> >> Best,
> >>
> >> É.
> >>
> >>
> >> _______________________________________________
> >>
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> >
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> >
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