A042944 Curvatures in diagram constructed by inscribing 2 circles of curvature 2 inside circle of curvature -1, continuing indefinitely to inscribe circles wherever possible.

-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

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,..., which would give A218155. However, some curvatures (starting with 78, listed in A042945) are in that 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 219-220.

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, arXiv:math/0009113 [math.NT], 2000-2003; J. Number Theory, 100 (2003), 1-45.

I. Peterson, Circle Game, Science News, 4/21/01.

Eric Weisstein's World of Mathematics, Bowl of Integers.

Crossrefs

Cf. A042945, A042946, A045506, A218155.

Sequence in context: A361103 A294510 A218155 * A361124 A163781 A090304

Adjacent sequences: A042941 A042942 A042943 * A042945 A042946 A042947

Keyword

sign,nice

Author

Brian Galebach, Allan Wilks

Status

approved