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John Derbyshire's Math Notes
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August 30, 2015, 07:11 PM
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itsnowonlineCan you figure out the next term in each of the following sequences?  Answers at the end.

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.