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%I #4 Mar 30 2012 17:27:18
%S 3,5,6,9,10,12,15,17,24,25,27,30,33,34,39,40,42,45,48,50,51,60,63,65,
%T 66,68,69,70,72,75,78,80,81,95,96,111,119,120,123,125,126,129,130,132,
%U 135,136,144,159,160,174,175,177,180,183,185,186,187,189,190,192,195,204
%N n-th even number equals n-th multiple of a Fermat number.
%C Sequence includes only multiples of Fermat numbers (sequence A080307), but not all of them. It is not certain that A080309 is infinite, but it seems likely given that exactly one-half of all integers are multiples of Fermat numbers (see A080307).
%e The first 3 even numbers are 2, 4 and 6; the first 3 multiples of Fermat numbers (the numbers of the form 2^(2^n)+1) are 3, 5 and 6. The third even number is also the third Fermat multiple; thus 3 is in the sequence.
%Y Cf. A000215 (the Fermat numbers), A080307.
%K nonn
%O 1,1
%A _Matthew Vandermast_, Feb 16 2003
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