   A problem
  The one will solve the problem will get a cookie:It does not matter what you will reach in your life, but the way you will reach it 
  I don''t think I''m getting this, but:if N(0) = 5 thenN(1) = 5 + 1 = 6N(2) = 6 + 3 + 2 + 1 = 12N(3) = 12 + 6 + 4 + 3 + 2 + 1 = 27Which  means N(3) = 27 which is not 15.I''m sure there is deeper meaning behind this, but that''s what I got. It seems to work for other numbers - 2~4, 7~8 etc. Well, I don''t get it! But I tried!  Yes... VB6 is here to steal your minds. Very slowly. ;  Not sure I understand this well but could it be...--------------------------N0 = 2N1 = 2 + 1 = 3N2 = 3 + 1 = 4N3 = 4 + 2 + 1 = 7N4 = 7 + 1 = 8N5 = 8 + 4 + 2 + 1 = 15 =>...--------------------------N0 = 3 N1 = 3 + 1 = 4N2 = 4 + 2 + 1 = 7N3 = 7 + 1 = 8N4 = 8 + 4 + 2 + 1 = 15 =>...--------------------------N0 = 4N1 = 4 + 1 = 5N2 = 5 + 1 = 6N3 = 6 + 3 + 2 + 1 = 12 => 1+2 = 3 (...the sum of the digits...)N4 = 3 + 1 = 4N5 = 4 + 2 + 1 = 7N6 = 7 + 1 = 8N7 = 8 + 4 + 2 + 1 = 15 =>...--------------------------N0 = 5 N1 = 5 + 1 = 6N2 = 6 + 3 + 2 + 1 = 12 => 1+2 = 3N3 = 3 + 1 = 4N4 = 4 + 2 + 1 = 7N5 = 7 + 1 = 8N6 = 8 + 4 + 2 + 1 = 15 =>...--------------------------N0 = 6N1 = 6 + 3 + 2 + 1 = 12 => 1+2 = 3N2 = 3 + 1 = 4N3 = 4 + 2 + 1 = 7N4 = 7 + 1 = 8N5 = 8 + 4 + 2 + 1 = 15 => 1 + 5 = 6N6 = 6 + 3 + 2 + 1 = 12 => 1+2 = 3N7 = 3 + 1 = 4N8 = 4 + 2 + 1 = 7N9 = 7 + 1 = 8N10 = 8 + 4 + 2 + 1 = 15 ( Oh very strange... )....Is this correct ?   [edited by - DarkPixel on February 4, 2004 7:45:31 AM];  The sequence is not monotonic.  Also I think N(3) is 19, it''s the sum of the digits, not just the divisors.  Notice that 15 does go to 15, one line of attack to the problem could be to show there are no other numbers that form cycles in the series, then show that above a certain value, the next term must be lower than the last, so it is bounded.  Leaving a finite number of possibilities and no other cycles, 15 must come up sooner or later.Of course it could be the case that one of my possibilities is false, which would complicate matters somewhat.  Fiddling about with the numbers may of course turn up a nice trick to solve it.Where did that problem come from?  It''s not very nicely or formally written.  Interesting though, if it wasn''t for the fact that I have two example sheets to do in the next few hours I would take a proper look. ;  You''re right but you did not solve it BTW: In the last sequence N10=N11=...=N1000000=...=15   It does not matter what you will reach in your life, but the way you will reach it ;  I''m closing this thread. The problem as stated appears to be a homework problem---even appears to be a scan from a textbook. Even if it is not homework, it violates forum policy (see link below) since it has every appearance of being homework or schoolwork. Review the forum FAQ for details on the policy.Forum FAQ Graham RhodesSenior ScientistApplied Research Associates, Inc. 