Geeky Thoughts and Sequences

Once I found myself wrestling with a collection of Internet brainteasers that included some of the most difficult integer sequence challenges I've ever encountered. Correct answers weren't returned in response to submitted entries, which prompted me to search the AT&T sequence database to check some of my answers.

When I searched for the answer to one particular sequence, I found a comment in the database noting that many people had requested the answer and that the answer remained unknown. Quite certain I had the answer, I felt a little puffed up, but I didn't add it to the database, because I didn't want compromise the test.

Later, I regretted the decision, because the author soon decided his test had been compromised and refused any subsequent entries. Not long after that, someone else claimed credit for the solution in the database. (Of course, the author of the test is certainly most worthy of credit.)

The sequence in question follows:

6, 8, 5, 8, 4, 0, 7, 3, ?

Turn to the AT&T Online Encyclopedia of Integer Sequences for the answer.

Yesterday, I thought of a sequence I'd like to see devilishly included on one of these tests. I believe the answer will come effortlessly to some who normally find sequence puzzles difficult. At the same time, I can imagine it leaving the sharpest young math whizzes throwing up their arms in dismay:

8, 6, 7, 5, 3, 0, ?

You'll find the answer to this one in the AT&T database as well.

Cheers.

1/7/2006. Update (thanks to ABC's Lost): 4, 8, 15, 16, 23, ?