13 Apr
2005
13 Apr
'05
11:17 a.m.
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.