1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1.

Jack,
Though it is not a race, you can see that a correct solution was first posted by Liz.  Liz's solution is not exactly the same as Juggler's unposted solution (as a Journeyman I was able to peek at the solution in queue), though both solutions are listed in the same integer sequence, A000265, as listed in The On-Line Encyclopedia of Integer Sequences, with Juggler ending his sequence at the 32nd term.

It is usually the policy of Perplexus that "official" solutions are posted by the problem submitter.  As of today, Juggler has not visited Perplexus for a little over 630 days, and so this problem's "official" solution may not be released until a Scholar has determined that Juggler will not return and that either the solution as-is is ready,  or that one will need to be written for the absentee, or one is linked to one of the correct solutions by one of the problem's solvers.