What follows in this sequence?

1, 2, 3, 3, 2, 3, 4, 5, 3, 2, 3, 4, 5, 5, 4, 5, 6, 7, 5, 4, 5, ...

1,2,3,3,2,3,4,5,3,2,3,4,5,5,4,5,6,7,5,4,5,6,7,7,6,7,8,9,7,6,7,8,9

Consider the Bold numbers first. The first triplet ends in 3. The next triplet begins with 3 and ends with 5.  This triplet is repeated whereupon the next triplet begins with the last digit of the previous triplet (and this triplet is also repeated).

Between these triplets, the sequence of odd numbers is paired with the sequence of even numbers (the even number is 1 less than the odd number).  Each of these pairings is repeated.

This array may clarify my thoughts:
1,2,3  3,2     3,4,5   3,2
3,4,5  5,4     5,6,7   5,4
5,6,7  7,6     7,8,9   7,6
7,8,9  9,8  9,10,11  9,8

In fact, if I consider 1,2,3,   3,2  3,4,5,  3,2 as being M, where M is the given set of digits,  each set of M (including my intial set) would be given by M + 2*x  where x = 0 to ....

Edited on August 2, 2005, 8:38 am

Edited on August 2, 2005, 8:48 am

Posted by brianjn on 2005-08-02 05:32:46