Should this sequence be in OEIS ? At present it appears as `denominators pf continued fraction convergents to sqrt(n)' for n = 159 A041293 n = 376 A041713 n = 467 A041891 n = 806 A042555 n = 937 A042813 !! R. On Wed, 13 Sep 2006, Daniel Asimov wrote:
Puzzle: What do the positive integers 1, 2, 3, 5, 18 have in common with each other, but with no other positive integer (conjecturally) ?
Hint: These number are cycle lengths.
The answer is: 1, 2, 3, 5, 18 are the cycle lengths of the 5 known (and conjecturally, only) cycles of the Collatz function f: Z -> Z when iterated, where f(n) is defined as
f(n) = n/2 if n is even; f(n) = 3n+1 if n is odd.
The cycles -- of lengths 1, 2, 3, 5, 18 -- are those containing 0, -1, 1, -5, -17, respectively.
--Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun