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

Author

Brian Galebach, Allan Wilks

Keywords

• sign
• nice

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.