[seqfan] Re: Dual sequences A214094 and A214156
Vladimir Shevelev
shevelev at bgu.ac.il
Sat Feb 23 16:57:47 CET 2013
By my request, Peter Moses considered initials (prime(n),prime(n+1)) up to n=209, i.e., up to initials (1289,1291). Every time he obtained eventually periodic sequences with the same length 36 of period. The sequence of maximal terms of these sequences I submitted as A221218.
Regards,
Vladimir
----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Wednesday, February 20, 2013 23:54
Subject: [seqfan] Re: Dual sequences A214094 and A214156
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> An interesting question: is 36 a special constant for
> neighboring primes?
> Since A214156 has period of length 36, I tried to consider
> sequences with the same rule but with another initials hoping to
> find periods with other lengths. I considered initials (2,3),
> (3,2), (3,5), (5,3),
> (5,7),(7,5),(7,11),(11,7),(11,13),(13,11),(13,17),(17,13),(17,19),(19,17),(19,23),(23,19). But every time I obtained period of length 36(!). It is interesting, when this chain will be btoken and what periods with other lengths we obtain in such case? I ask anyone to verify my handy calculations and possibly to continue them.
>
>
> Regards,
> Vladimir
>
>
> ----- Original Message -----
> From: Vladimir Shevelev <shevelev at bgu.ac.il>
> Date: Saturday, February 16, 2013 5:40
> Subject: [seqfan] Dual sequences A214094 and A214156
> To: seqfan at list.seqfan.eu
>
> > Dear SeqFans,
> >
> > I submitted two dual analogs of Fibonacci numbers without
> > semiprimes. They are
> > A214094: a(0)=0, a(1)=1; a(n)=a(n-1)+a(n-2), if a(n-1)+a(n-2)
> is
> > not semiprime; a(n)is maximal prime divisor of a(n-1)+a(n-2),
> if
> > a(n-1)+a(n-2) is semiprime;
> > A214156: a(0)=0, a(1)=1; a(n)=a(n-1)+a(n-2), if a(n-1)+a(n-2)
> is
> > not semiprime; a(n)is minimal prime divisor of a(n-1)+a(n-2),
> if
> > a(n-1)+a(n-2) is semiprime.
> > In case of A214156 I found that the sequence has period of
> > length 36 and thus is bounded. Can anyone try to find a period
> > for A214094 or at least indicate possible large limits where a
> > period not appears.
> >
> > Regards,
> > Vladimir
> >
> > Shevelev Vladimir
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> Shevelev Vladimir
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
Shevelev Vladimir
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