I was nosing around my home directory, and ran into a file with the following contents:

From The Mathematical Intelligencer, vol. 3, number 1, p. 45.

Problem is by J. H. Conway.

Problem 2.4:

A Prime Problem for the Ambidextrous

17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1.

Write down 2 (with your right hand). Look at these fourteen fractions and use them to generate two sequences of natural numbers by iterating the following:

If r is the last number you wrote with your right hand, look for the first of the fourteen fractions which, when multiplied with r, gives you an integer. Write the integer down (with your right hand). If this integer is a power of 2, say 2l, write down l (with your left hand).

  1. What is the left-hand sequence?
  2. Why?
  3. How long does it take to generate the first 1000 primes this way?

I’ve just spent a while working through it; I’m not done yet, but I’ve decided it’s interesting enough that there was a reason why I kept it lying around, and perhaps some of my blog readers might enjoy it.

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