What are the next two numbers in these two related sequences?

1 , 4 , 3 , 11 , 15 , 13 , 17 , --- , ---
10 , 9 , 60 , 90 , 70 , 66 , 69 , --- , ---

(In reply to Solution To The First Part by K Sengupta)

Let the ith term of the given sequence be T(i).

Then, T(i) = largest positive integer whose spelled out version
contain precisely (i+2) letters.

For example, the first term of the sequence is 01, which is spelled out as "ten",which contains 3 letters. Therefore, T(1) = 3.

Similarly, T(2) = 9, T(3) = 60, and so on..

We now observe that 99 is spelled out as "ninety nine" which contains precisely 10 letters and the spelled out version of any positive integer greater than 99 cannot contain precisely 10 letters.

Consequently, T(8) = 99

Again 10,000,000,000,000 is spelled out as "ten trillion" which contains pecisely 11 letters,and the spelled out version of any positive integer greater than this cannot contain precisely 11 letters.

Accordingly, T(9) =  10,000,000,000,000

Consequently, the required missing terms are 99 and 10,000,000,000,000.

Edited on May 27, 2008, 4:06 pm

Posted by K Sengupta on 2008-05-27 15:59:22