Give the next few numbers in this sequence and say what the sequence is:
1, 7, 3, 58, 19, 8, 5, 10, 70, 428, 10, 70, 119, 10, 70

(In reply to A guess by Leming)

I agree with your guess.  Here's why:

Let's start with the new sequence you found by adding the adjacent terms of the original sequence:

1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888

The 7th, 8th, and 9th terms are created by successively inserting a "0", then a "1", then an "8" into the third term, 11.

The next three terms are made in the same manner, by inserting 0, 1, and 8 into the fourth term, 69.

The next three terms are likewise found by inserting 0, 1, and 8 into the fifth term, 88.

So, it makes perfect sense to do the same with the sixth term, 96, to come up with the next three new terms.  Doing so we get:  906, 916, and 986.

From here, we can work backwards, taking the differences between adjacent terms in the new sequence to determine the next three terms of the original sequence.

This gives 18, 10, 70 for the next three, just as Leming guessed.

 

Posted by Mindrod on 2006-01-29 20:23:31