[seqfan] Re: Coprime To Sums

[zak seidov]

See A162842,
Zak

--- On Sun, 8/30/09, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> Subject: [seqfan]  Coprime To Sums
> To: seqfan at seqfan.eu
> Date: Sunday, August 30, 2009, 12:08 PM
> I think this sequence was worth
> submitting during Neil's vacation.
> 
> %I A164901
> %S A164901 1,2,4,7,13,19,29,37,43,53,59
> %N A164901 a(1)=1, a(2) = 2. For n >=3, a(n) = the
> smallest integer > a(n-1) that is coprime to every
> sum of any two distinct earlier terms of this sequence. 
> %e A164901 The first 4 terms are 1,2,4,7. The sums of every
> pair of distinct terms are: 1+2=3, 1+4=5, 2+4=6, 7+1=8,
> 7+2=9, and 7+4=11. So, we are looking for the smallest
> integer > 7 that is coprime to 3, 5, 6, 8, 9, and 11.
> This number, which is a(5), is 13. 
> %Y A164901 A164902,A164903 
> %K A164901 more,nonn
> %O A164901 1,2
> 
> (A164902 is the sequence of positive integers that each
> occur at least once as a sum of any two terms of A164901.
> A164903 is the compliment of A164902.)
> 
> I am surprised that this sequence isn't already in the
> OEIS. Even though I double-checked my work, did I make a
> mistake?
> 
> Second, Are there any more composites in the sequence? If
> so, are there an infinite number of composites? If so, could
> someone please calculate a number of terms of the sequences
> where one sequence contains the primes of A164901, and the
> other sequence contains the composites?
> 
> Thanks,
> Leroy Quet
> 
> 
> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] )
> ]
> 
> 
>       
> 
> 
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