# [seqfan] Re: Dual sequences A214094 and A214156

Vladimir Shevelev shevelev at bgu.ac.il
Thu Feb 21 12:53:29 CET 2013

```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,

----- 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,