

A042944


Curvatures in diagram constructed by inscribing 2 circles of curvature 2 inside circle of curvature 1, continuing indefinitely to inscribe circles wherever possible.


12



1, 2, 3, 6, 11, 14, 15, 18, 23, 26, 27, 30, 35, 38, 39, 42, 47, 50, 51, 54, 59, 62, 63, 66, 71, 74, 75, 83, 86, 87, 90, 95, 98, 99, 102, 107, 110, 111, 114, 119, 122, 123, 126, 131, 134, 135, 138, 143, 146, 147, 150, 155, 158, 162, 167, 170, 171, 174, 179, 182, 183
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OFFSET

1,2


COMMENTS

The sequence seems to follow a pattern where differences between consecutive terms are 3,1,3,5,3,1,3,5,.... However, some curvatures (starting with 78) are in the parent sequence, but missing from the circle diagram.


REFERENCES

Clifford A. Pickover, The Mathematics of OZ, Mental Gymnastics From Beyond The Edge, Cambridge University Press, Chapter 104 'Circle Mathematics,' figure courtesy of Allan Wilks, Cambridge, UK, 2002, pages 219220.


LINKS

James Spahlinger, Table of n, a(n) for n = 1..10000
R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks, and C. H. Yan, Apollonian Circle Packings: Number Theory, J. Number Theory, 100 (2003), 145.
I. Peterson, Circle Game, Science News, 4/21/01.
Eric Weisstein's World of Mathematics, Bowl of Integers.


CROSSREFS

Cf. A042945, A042946, A045506.
Sequence in context: A018687 A294510 A218155 * A163781 A090304 A005211
Adjacent sequences: A042941 A042942 A042943 * A042945 A042946 A042947


KEYWORD

sign,nice


AUTHOR

Brian Galebach, Allan Wilks


STATUS

approved



