A. 0, 1, 1, 2, 3, 5, 8, ...
B. 1, 7, 11, 27, 77, 111, 127, ...
C. 50, 40, 27, 36, ...
D. 3, 4, 7, 29, ...
Wired magazine last week offered a belated celebration of the 50th anniversary of the Encyclopedia of Integer Sequences, which started out as a book —I still have my 1995 edition—but nowadays of course is the On-Line Enyclopedia of Integer Sequences. Mathematician Neil Sloane got the ball rolling in 1964.
I have an entry in the OEIS: see "LINKS" here.
Not quite in the same league as having a theorem named after one, or having a poem in the Oxford Book of English Verse, but at this point I'll take what I can get.
Answers:
A. The Fibonacci sequence: each number is the sum of the two previous.
B. 177. The smallest whole number that needs n syllables to pronounce it in American English, for n = 1, 2, 3, ...
C. 34. Number of chapters in the n-th book of the Bible (KJV) for n = 1, 2, 3, ...
D. 20035299304068464649 ... (19,689 digits omitted here) ... 45587895905719156733. Values of Ackerman's function A(n,2) for n = 0, 1, 2, 3, ... Just screwin' with ya.