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

[M. F. Hasler]

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:
>>
>> 3141592653589793238462643383279502884197169399375105820974944592307816
>> 4062862089986280348253421170679821480865132823066470938446095505822317
>> 25359408128481117450284102701938
>>
>>
>>
>> Step 2 - I insert the divide sign "/" somewhere to produce a fraction:
>>
>> 3141592653589793238462643383279502884197169399375105820974944592307816
>> 406286208/998628034825342117067982148086513282306647093844609550582231
>> 725359408128481117450284102701938
>>
>>
>>
>> Step 3 - The fraction = 3.1459...
>>
>>
>>
>> Can you beat that? (this is, get closer to Pi)?
>>
>>
>>
>> Best,
>>
>> É.
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
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