The following are the smallest 9 elements of an infinite set of integers:

0,1,5,6,25,76,376,625,9376

What rule generates the set? What are the next two values?

The pattern I see is clunky and therefore probably not correct, but here goes:

Start with the terms 0, 1, 5, and 6 as given. The 5th term of the sequence is the square of the 3rd term, and the 8th term (5+3) is the square of the 5th term, so I would expect the 13th term (8+5) to be the square of the 8th term, or 390625.

Now, for the terms in between, ignore the terms discussed so far (which all end in 5), add the other earlier terms in the sequence, take the last digit, and place it in front of the last unignored term.

Thus, the 6th term is the last digit of (0+1+6) in front of 6, or 76.
The 7th term is the last digit of (0+1+6+76) in front of 76, or 376.
The 9th term (we are ignoring the 8th) is the last digit of (0+1+6+76+376) in front of 376, or 9376.

Following this (strained) logic, the next two terms will be 59376 and 159376.

I await a more elegant solution. lol

Posted by Bryan on 2003-03-14 06:39:16