What are the next two numbers in this sequence? 1, 2, 3, 5, 6, 9, 10, 15, 18, 24, 25, 34, 35, ??, ??

Assign each term a numerical value, starting with 1 as term one. Each term is then found by adding the previous term to the term in the place of that terms highest factor. For example, term eight is found by adding term seven to term four (four is eight's greatest factor). If the term number is prime, add term one (which is of course just one).
Observe:

Term    Highest Factor  Value
1                       1
2       prime -> 1      1+1 = 2
3       prime -> 1      1+2 = 3
4       2 -> 2          2+3 = 5
5       prime -> 1      1+5 = 6
6       3  -> 3         3+6 = 9
7       prime -> 1      1+9 = 10
8       4 -> 5          5+10 = 15
9       3 -> 3          3+15 = 18
10      5 -> 6          6+18 = 24
11      prime -> 1      1+24 = 25
12      6 -> 9          9+25 = 34
13      prime -> 1      1+34 = 35
...
14      7 -> 10         10+35 = 45
15      5 -> 6          6+45 = 51
16      8 -> 15         15+51 = 66

Therefore, the next two terms in the sequence are 45 and 51.

Posted by DJ on 2003-07-11 18:06:13