Here is my sequence (finite):
19,499,12991,337787,8782467,228344156,5936948059,154360649539.
You just have to figure out its logic.
Hint:
It is a "sequence" and I like alphabets.
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$\begingroup$ I thought about adding a sequence tag, but we don't have one that is generic. I will leave it off, assuming that either 1) none of the individual tags match your puzzle, or 2) tagging as such would be a dead give-away $\endgroup$ – Brian Robbins May 1 '15 at 14:57
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$\begingroup$ This is such a simple idea - I'm amazed nobody's posted a puzzle like this before! +1 and kudos to you $\endgroup$ – Rand al'Thor May 1 '15 at 15:44
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For ADG1, the logic is:
Convert all of the numbers to base 26, and convert each place in each number using A = 1, B = 2, etc. ADG1 then becomes
S, SE, SEQ, SEQU, SEQUE, SEQUEN, SEQUENC, SEQUENCE
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$\begingroup$ @ADG Yeah, I admit I don't think I'd have approached it the way I did without the hint, and with the hint it kinda fell into place for me. $\endgroup$ – Dennis Meng May 1 '15 at 14:55
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$\begingroup$ @ADG The hint seemed right to me, Dennis just did a great job of solving. $\endgroup$ – Joffan May 1 '15 at 15:00
