# [seqfan] Re: A178375

Wed May 26 18:13:46 CEST 2010

```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.

----- 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!
>
> ----- 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,
> >
> >
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> >
>