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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

%I #51 Aug 11 2020 11:12:19

%S -1,2,3,6,11,14,15,18,23,26,27,30,35,38,39,42,47,50,51,54,59,62,63,66,

%T 71,74,75,83,86,87,90,95,98,99,102,107,110,111,114,119,122,123,126,

%U 131,134,135,138,143,146,147,150,155,158,162,167,170,171,174,179,182,183

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

%C 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.

%D 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.

%H James Spahlinger, <a href="/A042944/b042944.txt">Table of n, a(n) for n = 1..10000</a>

%H R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks, and C. H. Yan, <a href="http://arxiv.org/abs/math/0009113">Apollonian Circle Packings: Number Theory</a>, arXiv:math/0009113 [math.NT], 2000-2003; J. Number Theory, 100 (2003), 1-45.

%H I. Peterson, <a href="http://web.archive.org/web/20030402151909/http://www.sciencenews.org/20010421/bob18.asp">Circle Game</a>, Science News, 4/21/01.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BowlofIntegers.html">Bowl of Integers.</a>

%Y Cf. A042945, A042946, A045506, A218155.

%K sign,nice

%O 1,2

%A _Brian Galebach_, _Allan Wilks_

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