John Derbyshire’s Math Notes


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.