[seqfan] Re: K-tuples in A180328

[Vladimir Shevelev]

Zak, it is a good idea!

I think that in connection with this one can consider a sequence: a(n) is the least semiprime p*q such that there are exactly n semiprimes different from a(n):  r_1*s_1,...,r_n*s_n with 
(p+1)*(q+1)=(r_i+1)*(s_i+1), i=1,...,n, and a(n)=0, if such semiprime does not exist.

Quetion: is a(n) always positive?

Regards,
Vladimir

----- Original Message -----
From: zak seidov <zakseidov at yahoo.com>
Date: Wednesday, September 8, 2010 14:29
Subject: [seqfan]  K-tuples in A180328
To: seqfaneu <seqfan at seqfan.eu>

> K-tuples in A180328
> 
> In A180328 we have not only pairs, e.g., 
> 14,15: s=(2+1)(7+1)=(3+1)(5+1)=24
> 
> but also triples, e.g., 46,51,55: 
> s=(2+1)(23+1)=(3+1)(17+1)=(5+1)(11+1)=72
> 
> quadruples, e.g., 94,115,119,121: 
> s=(2+1)(47+1)=(5+1)(23+1)=(7+1)(17+1)=(11+1)(11+1)=144....
> and even 36-tuples, e.g., 
> 6652798,9147589,9563377,9752357,9812821,9840529,9854381,9860317,9868231,
> 9886693,9919633,9923581,9934427,9937381,9941137,9955669,9956081,9957139,
> 9957931,9961969,9964621,9965471,9966787,9970021,9970321,9970673,9971089,
> 9971317,9971771,9971953,9972031,9972181,9972349,9972643,9972871,9972877
> with  s=9979200. 
>   What about 100-tuples, 1000-tuples, etc?
> Zak
> 
> 
>       
> 
> 
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 Shevelev Vladimir‎