[seqfan] Re: Dual sequences A214094 and A214156

[Vladimir Shevelev]

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
> 
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 Shevelev Vladimir‎