A202138 Numerators of Conway's PRIMEGAME.

17, 78, 19, 23, 29, 77, 95, 77, 1, 11, 13, 15, 1, 55

Offset

1,1

Comments

Denominators are in A203363.

Conway's PRIMEGAME (also called "Conway's prime producing machine") is a fascinating (and very inefficient) method for obtaining the prime numbers.

The "machine" consists of 14 rational numbers. Starting with 2, one searches the first number in the machine that multiplied by 2 gives an integer; then for that integer we search the first number in the machine that generates another integer. This process (corresponding to the successor function A203907) is repeated for each new integer obtained. Thus A007542 is generated. Except for the initial 2, each number in A007542 having an integer binary logarithm is a prime number.

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.

Links

Table of n, a(n) for n=1..14.

J. H. Conway, FRACTRAN: a simple universal programming language for arithmetic, in T. M. Cover and Gopinath (Eds.), Open Problems in Communication and Computation, Springer, NY, 1987, pp. 4-26.

R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33.

Prog

(Haskell)
a202138_list = [17, 78, 19, 23, 29, 77, 95, 77, 1, 11, 13, 15, 1, 55]
-- Reinhard Zumkeller, Jan 24 2012
(Python) see A203907.

Crossrefs

Cf. A007542 (trajectory of 2 under iterations of A203907), A007546, A007547.

Cf. A203363 (denominators), A203907 (the PRIMEGAME successor function).

Sequence in context: A231779 A063494 A146594 * A357740 A124898 A036429

Adjacent sequences: A202135 A202136 A202137 * A202139 A202140 A202141

Keyword

nonn,frac,fini,full

Author

Alonso del Arte, Dec 31 2011

Status

approved