Let's look at the sequence with terms
a
_{1}=19,
a
_{2}=95, and a
_{n+2}=LCM(a
_{n+1},a
_{n})+a
_{n}
LCM stands for Least Common Multiple, and n is a positive integer.
Find the Greatest Common Divisor (GCD) of terms a_{4096} and a_{4097}.
(In reply to
re(2): Just a guess...  proof by Richard)
Yes, that's what I'm saying: that any factor of a(n+2) and a(n+1) is a factor of a(n), as a(n+2) = a(n)*(u2+1), where u2 is LCM(a(n),a(n+1))/a(n) and so contains the factors of a(n+1) that are not factors of a(n). Adding 1 to this in forming a factor of a(n+2) prevents n+2 from having factors common to a(n+1) that are not factors of a(n).

Posted by Charlie
on 20060819 19:18:23 