hihi, all - rkg@cpsc.ucalgary.ca wrote ...

[define a sequence by] a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

This leads to 1,2,3,4,7,8,11,12,18,24,30,41,42,55,...

The original problem asked that if you start elsewhere, e.g.,

5,6,12, ... or 9,13,14,24, ... or 10,18, ... or 15,24, ...

do you always merge with the original sequence? Evidently

91,112,122,186,... takes a little while.

... i wrote a simple program to compute these sequences, but only with 1003 primes, and all of the sequences merged with the original a[0]=1 sequence up to a[0]=393 (starting with a[0]=91 takes 24 terms, starting with a[0]=105 takes 41, both local maxima) presumably this can be easily extended more later, cal