[seqfan] Re: A fractal seq with (primes by concatenation) pairs

[M. F. Hasler]

But why 1,3 and not 0,13 ?
M.
Le 19 août 2015 18:09, "Eric Angelini" <Eric.Angelini at kntv.be> a écrit :

> Hello SeqFans,
>
> Pr = 0,2,0,0,3,2,0,5,0,0,7,0,1,3,3,2,3,2,1,1,0,1,7,5,1,9,0,4,1,0,4
> ,7,7,2,9,0,8,9,1,4,3,3,5,3,3,3,1,2,5,9,3,3,7,2,7,9,1,10,9,1,6,1,0,
> 1,37,1,6,7,7,7,1,5,1,39,1,8,3,9,9,7,0,10,1,4,14,9,1,10,3,0,10,7,4,
> 12,7,7,15,7,7,7,3,2,1,31,9,1,13,0,1,51,8,1,63,9,1,67,1,17,3,4,17,9,
> 3,19,3,3,18,1,5,1,91,3,19,9,3,22,3,3,2,11,1,19,7,2,2,27,5,2,29,9,2,
> 33,3,2,39,3,2,41,7,2,51,2,25,7,7,2,63,9,26,9,1,2,71,10,2,77,9,2,83,
> 1,2,81,6,...
>
> Erase all pairs of terms forming a prime by concatenation;
> the remaining terms will reproduce the original sequence:
>
> Pr =
> (0,2),0,(0,3),2,(0,5),0,(0,7),0,(1,3),3,(2,3),2,(1,1),0,(1,7),5,(1,9),0,...
>
> We consider here that (0,2), for instance, represents the prime "2"
> and (0,3) the prime "3", etc. We see that the 5th "prime" (1,3) is
> not (1,1); this is because (1,1) would have produced a "prime-overlap"
> with the following "3" : (1,1),3, --and we don't want such overlaps.
> So we took the next available "split-prime" to extend the sequence,
> which is "13".
> After "13" we could still not use "11" -- as we would have another
> overlap, but just before "11": 3,(1,1),2, -- indeed, 31 is prime.
> So we tried 17 and 19 (same problem) before choosing "23".
>
> How was Pr build? Pr is a succession of triplets s, t, u:
>
> s t u
> 0,2,0,
> 0,3,2,
> 0,5,0,
> 0,7,0,
> 1,3,3,
> 2,3,2,
> 1,1,0,
> 1,7,5,
> 1,9,0,
> 4,1,0,
> 4,7,7,
> 2,9,0,
> 8,9,1,
> 4,3,3,
> 5,3,3,
> 3,1,2,
> 5,9,3,
> 3,7,2,
> 7,9,1,
> 10,9,1,
> ...
>
> -- s concatenated with t always produces a prime (s,t);
> -- this (s,t) prime is always the smallest not yet present in Pr;
> -- the term just before s, concatenated to s, never produces a prime;
> -- t and u, concatenated, never produce a prime;
> -- there is no choice for u, because u is given by the seq itself
>    (as we want Pr to be "fractal)
>
> Best,
> É.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>