Unsolved? problem

[Richard Guy]

I'm collecting Murray Klamkin
problems and solutions and am
currently going thru Math Mag.

I came across Problem 886,
Math Mag 48(1975) 57--58
[nothing to do with Murray]
which isn't properly stated
but should read as in OEIS
A003508 :

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.

Has anyone ... Can anyone prove
Charles Trigg's guess ?    R.