[seqfan] Re: Concatenate 5 digits = prime
Jim Nastos
nastos at gmail.com
Thu Mar 26 20:03:43 CET 2009
If your sequence can start with 1,2,3,4,5,7... why doesn't Jean-Marc
Falcoz's sequence begin with: 1,2,3,4,7, since 12347 is a 5 digit
prime number?
JN
On Thu, Mar 26, 2009 at 11:52 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
>
> Jean-Marc Falcoz has computed this seq. :
>
> 1,2,3,7,19,31,91,373,931,1931,1933,7193,11931,19311,93119,311931,
> 913733,1373313,7331373,9311931,19311931,19311933,71931193,119311931,
> 193119311,931193119,3119311931,9137331373,9311931193,...
>
> ... where any concatenation of 5 consecutive digits is a prime.
>
> We clearly have a(1) = 1
> and a(n) smallest integer > a(n-1) not leading to an
> *immediate* contradiction
>
> Is the seq infinite?
>
> ---
>
> The seq where any concatenation of 6 consecutive digits is a prime
> stops immediately:
>
> 1,2,3,4,5,7
> the only possibility being 1,2,3,4,5,7,1 -- but no 6-digit prime
> starts with 34571-
>
> ... stops immediately unless we drop the above *immediate* constraint
> (but the resulting seq might be too heavy to compute with brute force
> (trials and errors).
>
> Best,
> É.
>
>
>
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