Re: Converging sum of reciprocals

In article <fvaq6r$89i$1@xxxxxxxxxxxxxxxx>,
"joeshipman@xxxxxxx" <JoeShipman@xxxxxxx> wrote:

Let X_3 be the set of positive integers constructed by sieving out all
integers that are the sum of two earlier ones in the set:
1,2,4,5,10,11,13,14,28,29,31,32,37,38,40,41,82,...

Then 5 shouldn't be in there, should it?

X_3 contains no arithmetic progressions of length 3.

Is there some connection between no number a sum of two others
and no 3-term arithmetic progressions?

The sum of the reciprocals of the first 2^16 elements of X_3 is
3.004209955... The Erdos-Turan conjecture states that any set of
positive integers whose sum of reciprocals converges contains
arbitrarily long arithmetic progressions,

I think you mean "diverges."

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)

.

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