-3,1

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^n-1)/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 [This has been replaced by 16 here to get an integer sequence.]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.

Roger Penrose, Twistor Newsletter, No. 10 (1980), p. 22.

Cf. A003138, A003176, A003177.

Sequence in context: A075335 A020720 A048589 this_sequence A112529 A161892 A056528

Adjacent sequences: A121053 A121054 A121055 this_sequence A121057 A121058 A121059

nonn

N. J. A. Sloane (njas(AT)research.att.com), Aug 10 2006