A121056 From a puzzle of Roger Penrose's in the Twistor Newsletter.

7, 9, 12, 16, 24, 36, 56, 90

Offset

-3,1

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^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 [This has been replaced by 16 here to get an integer sequence.]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.

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]

Crossrefs

Cf. A003138, A003176, A003177.

Sequence in context: A250220 A020720 A048589 * A174189 A112529 A352876

Adjacent sequences: A121053 A121054 A121055 * A121057 A121058 A121059

Keyword

nonn

Author

N. J. A. Sloane, Aug 10 2006

Status

approved