Strangers On A Train

October 27, 2015

In Sloane’s Encyclopedia, sequence A247665 is defined as

a(1) = 2; thereafter a(n) is the smallest number not yet used which is compatible with the condition that a(n) is relatively prime to the next n terms. The sequence begins 2, 3, 4, 5, 7, 9, 8, 11, 13, 17, 19, 23, 15, 29, 14, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, …

The sequence was submitted by Amarnath Murthy and given to Neil Sloane as a birthday present. Sloane calls the sequence “Strangers on a Train” after the psychological thriller novel by Patricia Highsmith and subsequent film by Alfred Hitchcock, because the nth element of the sequence has no factors in common with the next n elements (they are “strangers”).

Your task is to write a program that generates the sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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