cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A042944 #52 Feb 16 2025 08:32:38
%S A042944 -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 A042944 71,74,75,83,86,87,90,95,98,99,102,107,110,111,114,119,122,123,126,
%U A042944 131,134,135,138,143,146,147,150,155,158,162,167,170,171,174,179,182,183
%N A042944 Curvatures in diagram constructed by inscribing 2 circles of curvature 2 inside circle of curvature -1, continuing indefinitely to inscribe circles wherever possible.
%C A042944 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 A042944 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 A042944 James Spahlinger, <a href="/A042944/b042944.txt">Table of n, a(n) for n = 1..10000</a>
%H A042944 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 A042944 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 A042944 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BowlofIntegers.html">Bowl of Integers.</a>
%Y A042944 Cf. A042945, A042946, A045506, A218155.
%K A042944 sign,nice
%O A042944 1,2
%A A042944 _Brian Galebach_, _Allan Wilks_