primes in pi: 1, 2, 6, 38, 16208, 47577, 78073, ...
Jonathan Post
jvospost3 at gmail.com
Tue Jul 25 01:14:45 CEST 2006
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Okay then Frank, your way (which is naturally natural) gives the sequence of
primes 3, 23, what's next?
from Ceiling(substrings of pi base e)
1 = 1*e^0 = 1
10 = 1*e^1 + -*e^0 = e represents 3 (which is prime)
101 = e^2+1 = 8.389... represents the number 9.
1010 ceil(22.803) = 23 (which is prime)
10101 gives 63 = 1*(e^4) + 0*(e^3) + 1*(e^2) + 0*(e^1) + 1 = 62.9872061
composite
101010 gives 172 = 1*(e^5) + 0*(e^4) + 1*(e^3) + 0*(e^2) + 1*(e^1) + 0*(e^0)
= ceil(171.216978) composite**
then 1010100 gives 466 = ceil(*465.41600) *
then 10101002 gives 1268 composite
then 101010020 gives 3445 composite
then 1010100200 gives 9363 composite
What are the next few primes? Is this an interesting sequence that you have
guided me to, as potential co-author?
My wife advises that Southern California Edison has restored power to our
home, roughly 72 hours since we lost it, so I'll be heading home now.
Best,
Jonathan Vos Post
On 7/24/06, franktaw at netscape.net <franktaw at netscape.net> wrote:
>
> No, no, no. Of course you want to look in base e. For any initial
> sequence, there is only one integer which has that as the part before
> the "decimal" point in base e: just take the ceiling. So, for example,
> 101 = e^2+1 = 8.389... represents the number 9.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Jonathan Post <jvospost3 at gmail.com>
>
> I am somewhat serious about pi base e. So far as I can see, pi base e
> = 10.101002020002111120020101120... as per A050948Pi expressed in base
> 1/e: Pi = Sum a(i)*exp(-i), i=-1,0,1,...
>
> Now, in what base should we examine substrings of this for primality?
> In the unnatural base 10, ...
>
>
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