[seqfan] Re: A178375

[Vladimir Shevelev]

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
> 
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 Shevelev Vladimir‎