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 , --- , ---

The 'official' solution is in error.

Each part is asking for the sequence of natural numbers of sequential length in its English spelling (as spelled out in letters only, that is, hyphens and spaces are excluded in the determination of length), and, as in the short scale, 100 is One Hundred and not simply, Hundred). The first part asks for the smallest of these numbers, and the second part, for the largest.

We can surmise that the sequence is limited to natural numbers from the first sequence {1, 4, 3, 11, 15, 13, 17, ...}, as 4 (four) is given as the second term instead of 0 (zero).

In the second sequence {10, 9, 60, 90, 70, 66, 69, ...}, where the seventh term, the number given for 9-letters, is given as 69 (Sixty-Nine), a possible mistake in transposition of digits may have occured. 96 (Ninety-Six) is also a number of 9-letters.  Still, there exists larger natural numbers of 9-letters. In the Myriad system, there is 10⁵ (Ten Myriad : 10,0000), and, in the standard system, an even larger number -- 10¹⁰¹ (Ten Googol).

The two numbers sought in the second sequence (the 10- and 11-letter numbers) are given in the 'official' solution as 99 (Ninety-Nine) and 10,000,000,000,000 (Ten Trillion : 10¹³), respectively. Yet, of the 10-letter numbers, a larger number exists in the standard system -- 10,000,000,000 (Ten Billion : 10¹⁰).

Edited on May 28, 2008, 10:05 am

Posted by Dej Mar on 2008-05-28 02:11:53