[math-fun] Unsolved? problem

[Richard Guy]

Thanks for several responses.
I've got as far as Math Mag
48(1975) 301 and find:

``C.W.Trigg, C.C.Oursler, and
R.Cormier & J.L.Selfridge have
sent calculations on Problem 886
[Nov 1973] for which we had
received only partial results
[Jan 1975].

Given an ... (restatement of
problem)

C & S sent the following results:
There appear to be 5 seqs beginning with
integers less than 1000 which do not merge.
These sequences were carried out to
10^8 or more.  The calculations are:

1,2,3,4,7,8,..,96532994,144799494,...(31)
393,528,545,660,682,727,...,97622612,
              122028268,... (9)
412,518,565,684,709,710,..., 92029059,
              102254514,... (46)
668,838,1260,1278,1355,1632,...,91127590,
              100240357,... (52)
932,1168,1244,1558,1621,1622,...,98457737,
              112523136,... (30)

The numbers in parens show the numbers
of terms between 50000000and 10^8.  The
rate of growth of these sequences suggests that
there are likely an inf no of mutually
indep seqs.

[[30 yrs on our computers, human &
electronic, shd be able to improve on
this.  Should the last 4 of the above
5 seqs be in OEIS ??    R.]]

On Wed, 13 Apr 2005, Richard Guy wrote:

> 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.
>
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