1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1.

we all noticed all numbers in the sequence is odd.

and the pattern are the following:

1st,

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1.

in (2n-1)th terms have the sequence of consecutive odd numbers.

2nd,

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1.

in (4n-2)th terms have also the sequence of consecutive odd numbers.

3rd,

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1.

in (8n-4)th terms have also the sequence of consecutive odd numbers.

in this 3 patterns of sequences, we conclude that [(2^k)n-(2^(k-1))]th terms where k = 1,2,3,...n starts with 1 followed by the next odd number 3 and so on to its preceeding term.

Edited on August 5, 2005, 9:13 am

Edited on August 6, 2005, 9:30 am

Posted by nickson on 2005-08-05 09:11:30