[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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