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

[Bob Selcoe]

Unless I'm mistaken, because that would mean s=1, t=13, u=3;  but 13 < 113, 
so t=3.

Cheers,
Bob S.

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From: "M. F. Hasler" <oeis at hasler.fr>
Sent: Wednesday, August 19, 2015 12:51 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Cc: "Alexandre Wajnberg" <alexandre.wajnberg at skynet.be>
Subject: [seqfan] Re: A fractal seq with (primes by concatenation) pairs

> 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.
>>
>>
>>
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>>
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>>
>
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