%I
%S 7,9,12,16,24,36,56,90
%N From a puzzle of Roger Penrose's in the Twistor Newsletter.
%C Roger Penrose posed the problem of finding the missing term in the sequence "..., 7, 9, 12, ???, 24, 36, 56, 90, ...".
%C 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 [This has been replaced by 16 here to get an integer sequence.]
%C 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.
%H R. J. Penrose, <a href="http://people.maths.ox.ac.uk/lmason/Tn/TN125/No10%202%20July%201980.pdf">Puzzle</a>, Twistor Newsletter, No. 10 (July 1980), p. 22.
%H R. J. Penrose, <a href="/A003138/a003138.pdf">Puzzle</a>, Twistor Newsletter, No. 10 (July 1980), p. 22. [Cached copy]
%H R. J. Penrose, <a href="http://people.maths.ox.ac.uk/lmason/Tn/41/TN41.pdf">Solution to puzzle</a>, Twistor Newsletter, No. 41, p. 37, 1996.
%H R. J. Penrose, <a href="/A003138/a003138_1.pdf">Solution to puzzle</a>, Twistor Newsletter, No. 41, p. 37, 1996. [Cached copy]
%Y Cf. A003138, A003176, A003177.
%K nonn
%O 3,1
%A _N. J. A. Sloane_, Aug 10 2006
