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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