[seqfan] Re: Pairwise sums are all semiprimes.

[Maximilian Hasler]

I get
a=[1,3,32,54]
then the sequence stops, because:

* if the next term is a(5)=2k+1, then
a(5)+a(1)=2(k+1)
a(5)+a(2)=2(k+2)
which cannot both be semiprime (since either k+1 or k+2 have a second factor 2)

* if the next term is a(5)=2k, then
a(5)+a(3)=2(k+16)
a(5)+a(4)=2(k+27)
which cannot both be semiprime (since either k+16 or k+27 have a
second factor 2).

So you might object that 54 is not the correct term.
But in view of what precedes, whatever you choose as preceding terms,
among a(1)..a(4) there are at least and at most 2 even and 2 odd terms
(using the same reasoning as above), and there is no possible 5th term.

Maximilian



On Sat, Jun 12, 2010 at 5:51 AM, zak seidov <zakseidov at yahoo.com> wrote:
> a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all semiprimes.
> 1,3,32,90
> more terms?
> Zak
>
>
>
>
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