
COMMENTS

Roger Penrose posed the problem of finding the missing term in the sequence "..., 7, 9, 12, ???, 24, 36, 56, 90, ...".
The answer is that the sequence is given by a(n) = 24*(2^n1)/n, for n = 3, 2, ..., 3, 4 and so the missing entry is (by l'Hopital's rule) 24 log 2 = 16.6355323... [This has been replaced by 16 here to get an integer sequence.]
The sequence for n = 10, ..., 10 is 3069/1280, 511/192, 765/256, 381/112, 63/16, 93/20, 45/8, 7, 9, 12, 24 log 2, 24, 36, 56, 90, 744/5, 252, 3048/7, 765, 4088/3, 12276/5.


LINKS

Table of n, a(n) for n=3..4.
R. J. Penrose, Puzzle, Twistor Newsletter, No. 10 (July 1980), p. 22.
R. J. Penrose, Puzzle, Twistor Newsletter, No. 10 (July 1980), p. 22. [Cached copy]
R. J. Penrose, Solution to puzzle, Twistor Newsletter, No. 41, p. 37, 1996.
R. J. Penrose, Solution to puzzle, Twistor Newsletter, No. 41, p. 37, 1996. [Cached copy]
