2 puzzles

[זקיר סעידוב - ד\"ר/Zakir Seidov Ph.D.]

1. I guess that 7 is too small number of terms:
   18, 9, 11, 14, 7, 9, 12

Take a[n]; 
A) if a[n]=even, then a[n+1]=a[n]/2, 
              else  {a[n+1]=a[n]+2, a[n+2]=a[n+1]+3}, now a[n+2] is even, -> A)

By this simple rule next terms are 6,3,5,8,4,2,1,3,(6,3,5,8,4,2,1,3)- cycle
and why not? 
Also note that 6 is in the list of possible answers.

2. I guess that 7 is too small number of terms:
All terms are even so first divide all them by 2:
   2, 6, 3, 6, 18, 9, 18

Take a[n]; 
A) If a[n] is even, then {a[n+1]=3*a[n], a[n+2]=a[n+1]/2],
              else a[n+1]=2*a[n], now a[n+1] is even, -> A)

By this simple rule next terms are 54,27,54,162,81,162,486,243,486,1458,729,1458...
and why not?

Also note that 54 (or 108 after multiplying by 2) 
is in the list of possible answers.

Two rules have  something common...
 
Zak

-----Original Message-----
From: N. J. A. Sloane [mailto:njas at research.att.com]
Sent: Friday, July 18, 2003 11:56 AM
To: seqfan at ext.jussieu.fr; somos at grail.cba.csuohio.edu
Subject: 2 puzzles


These just came in

I don't know the answers!

NJAS

Lookup  18, 9, 11, 14, 7, 9, 12
(Possible answers are: 5, 6, 14, 20

Lookup  4, 12, 6, 12, 36, 18, 36
(Possible answers are: 108, 112, 128. 130. 134