A Sequence Puzzle of my Own Devising

I was just fiddling with numbers recently and came up with the following sequence:
4, 5, 5, 6, 14, 11, 8, 11, 8, 8, 13...
Can anyone tell me what the next few terms in the sequence might be? Here's a cryptic hint: 'geometry'
Edit: There's a free cherry pie for whomever can get their mind 'round this puzzle and come up with the answer...
Edit: Cherry pi? Since I posted this puzzle, my sequence has been accepted to the Encyclopedia of Integer Sequences. To generate the sequence, take the digits of pi: 3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9... If you take the sum of each consecutive digit (3+1), (1+4), (4+1), (1+5) etc. you get 4, 5, 5, 6, 14 and so forth. So the next few terms are 17, 16, 16... And did anyone notice the time on the posting?

NPR Sunday Puzzle (Oct 30) - Eli, before and after

NPR Sunday Puzzle (Oct 30) - Eli before and after

Q: Take the name Eli and add three letters in front of it. Add the same three letters in reverse order after it to complete a familiar two-word phrase in nine letters. What is it?
Hint: The answer is something this puzzle has.

This one doesn't take much work to figure out. I found the hint wasn't that useful for finding the answer, but did serve as a confirmation, once I had found the answer. As always, I can't reveal my answer until after the deadline.
Edit: Your time is up!

TIM + ELI + MIT --> Time Limit

NPR Sunday Puzzle (Oct 16) - Multiplication Magic Square

NPR Sunday Puzzle (Oct 16) - Multiplication Magic Square

Q: In a standard 4 by 4 magic square you arrange the digits from one to sixteen so each row, column and corner diagonal totals 34. This is a multiplication magic square: Arrange sixteen numbers in a four by four square so that the product of each row, column and corner to corner diagonal is 5,040. You can use any numbers you want. But they have to be whole numbers and you can't repeat a number in the square. (And as a hint I'll tell you the number in the upper left corner is 42.)

Finally! A mathematical/number puzzle instead of a word puzzle! I do have an answer to the puzzle. In fact I have several since the answer is non-unique. In addition to solutions that have 42 in the upper left, and solutions that have 42 elsewhere in the puzzle, I found solutions that don't have 42 at all! As usual, I won't post any answers until after the deadline. My one hint: prime factorization.
Edit: Okay, after all that work and no one called me from NPR. Check the following PDF for the solution(s).

Magic Square Answer(s)

Edit: Since this posting, I've found 8 other arrangements that I previously missed (with 30 in them). That brings the total to 80, not 72.

NPR Sunday Puzzle (Oct 9) - Non-rhyming words starting M, N and ST

NPR Sunday Puzzle (Oct 9) - Non-rhyming words starting M, N and ST

Q: Take the words MAY, NAY, and STAY. Except for their opening letters, M, N and ST, they're spelled the same and they rhyme. Can you name three common, un-capitalized words, starting with M, N and ST, that again are spelled the same except for these opening letters? None of the words rhyme with any of the others. The lengths of the answers are for you to determine.

Initially, I figured the answers had to be one syllable and if MONE had been a word, I would have had NONE and STONE. Instead, the answer I came up with had two-syllables for each of the non-rhyming words. Can you come up with an answer? As always, I'll reveal my answer later in the week.
Edit: When will NPR ever call me? Not this week I guess so once again here's the answer I submitted.

A: MATURE, NATURE and STATURE are the three words I came up with that have the same ending but don't rhyme.