[seqfan] Re: A178375

[Vladimir Shevelev]

Once more, such conjecture is true for a close sequence, when instead of c(n) to consider C(n)=gcd(n, A000032(n)-1,A001608(n)):

A^*178375={2,3,2,5,1,7,2,3,1,11,1,13,1,1,2,17,1,19,1,1,2,23,1,5,1,3,1,29,1,31,2,1, 1,1,1,...},

i.e. A178375 and A^*178375 differ in points 33,35,...

Vladimir


----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Wednesday, May 26, 2010 19:27
Subject: [seqfan] Re: A178375
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Sorry, in the case when n does not divide neither  
> A000032(n)-1 nor A001608(n), why it does not exist a large prime 
> P which divides c(n)? I.e. the conjecture remains.
> 
> Vladimir
> 
> ----- Original Message -----
> From: Vladimir Shevelev <shevelev at bgu.ac.il>
> Date: Wednesday, May 26, 2010 18:28
> Subject: [seqfan] Re: A178375
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> 
> > Note that from the Bertrand's postulate it is easily follows 
> > that Conjecture in A178375, of course, is true!
> > 
> > Vladimir
> > ----- Original Message -----
> > From: Vladimir Shevelev <shevelev at bgu.ac.il>
> > Date: Wednesday, May 26, 2010 17:59
> > Subject: [seqfan]  A178375
> > To: seqfan at list.seqfan.eu
> > 
> > > Dear SeqFans,
> > > 
> > > I have just submitted the following sequence:
> > > 
> > > %I A178375
> > > %S A178375 
> > > 
> > 
> 2,3,2,5,1,7,2,3,1,11,1,13,1,1,2,17,1,19,1,1,2,23,1,5,1,3,1,29,1,31,2,7,%T A178375 1,3,1
> > > %N A178375 Let c(n)=gcd(A000032(n)-1,A001608(n)). Then 
> a(n)=1, 
> > > if c(n)=1; otherwise, a(n) is the maximal prime divisor of 
> > c(n) 
> > > [A000032=Lucas sequence; A001608=Perrin sequence] 
> > > %C A178375 If n is prime, then n divides c(n). We call n a 
> > Lucas-
> > > Perrin pseudoprime if n is composite and divides c(n). 
> > > Conjecture. Records of the sequence are consecutive primes. 
> > > %Y A178375 A000032 A001608 
> > > %K A178375 nonn
> > > %O A178375 2,1
> > > 
> > > Can anyone  find a few "Lucas-Perrin pseudoprimes" ? 
> (the 
> > > drfinition see in %C)
> > > 
> > > Regards,
> > > Vladimir
> > > 
> > >  Shevelev Vladimir‎
> > > 
> > > _______________________________________________
> > > 
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > > 
> > 
> >  Shevelev Vladimir‎
> > 
> > _______________________________________________
> > 
> > Seqfan Mailing list - http://list.seqfan.eu/
> > 
> 
>  Shevelev Vladimir‎
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
> 

 Shevelev Vladimir‎