A202138 Numerators of Conway's PRIMEGAME.

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

Offset: 1

Author

Alonso del Arte, Dec 31 2011

Keywords

• nonn
• frac
• fini
• full

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 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.

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

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

Crossrefs

Cf. A007546, A007547.

Programs

Haskell

a202138_list = [17, 78, 19, 23, 29, 77, 95, 77, 1, 11, 13, 15, 1, 55]
-- Reinhard Zumkeller, Jan 24 2012