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A080307 Multiples of the Fermat numbers 2^(2^n)+1.

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%I A080307 #8 Apr 25 2024 05:56:33
%S A080307 3,5,6,9,10,12,15,17,18,20,21,24,25,27,30,33,34,35,36,39,40,42,45,48,
%T A080307 50,51,54,55,57,60,63,65,66,68,69,70,72,75,78,80,81,84,85,87,90,93,95,
%U A080307 96,99,100,102,105,108,110,111,114,115,117,119,120,123,125,126,129,130,132
%N A080307 Multiples of the Fermat numbers 2^(2^n)+1.
%C A080307 Since all the Fermat numbers are relatively prime to each other (see link), the probability that a given integer is not a multiple of the first k Fermat numbers is 2^((2^k)-1) / 2^(2^k)-1, the limit of which is 0.5 as k increases infinitely; therefore the probability that an integer is a Fermat multiple, as well as the probability that it is not, is 0.5.
%H A080307 R. Munafo, <a href="http://www.mrob.com/pub/math/ln-notes1.html#fermat">Notes on Fermat numbers</a>.
%Y A080307 Cf. A000215, A080308, A080309.
%K A080307 easy,nonn
%O A080307 1,1
%A A080307 _Matthew Vandermast_, Feb 16 2003