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A202138 Numerators of Conway's PRIMEGAME.

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%I A202138 #27 Jun 09 2015 16:00:00
%S A202138 17,78,19,23,29,77,95,77,1,11,13,15,1,55
%N A202138 Numerators of Conway's PRIMEGAME.
%C A202138 Denominators are in A203363.
%C A202138 Conway's PRIMEGAME (also called "Conway's prime producing machine") is a fascinating (and very inefficient) method for obtaining the prime numbers.
%C A202138 The "machine" consists of 14 rational numbers. Starting with 2, one finds the first number in the machine that multiplied by 2 gives an integer; then for that integer we find the first number in the machine that generates another integer. This process is repeated for each new integer obtained. Thus A007542 is generated. Except for the initial 2, each number in A007542 having an integer for a binary logarithm is a prime number.
%C A202138 Note that in R. K. Guy's 1983 paper, the last four numbers of the machine are 13/11, 15/14, 15/2 and 55 rather than 13/11, 15/2, 1/7 and 55.
%H A202138 R. K. Guy, <a href="http://www.jstor.org/stable/2690263">Conway's prime producing machine</a>, Math. Mag. 56 (1983), no. 1, 26-33.
%o A202138 (Haskell)
%o A202138 a202138_list = [17, 78, 19, 23, 29, 77, 95, 77, 1, 11, 13, 15, 1, 55]
%o A202138 -- _Reinhard Zumkeller_, Jan 24 2012
%Y A202138 Cf. A007546, A007547.
%K A202138 nonn,frac,fini,full
%O A202138 1,1
%A A202138 _Alonso del Arte_, Dec 31 2011