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.

A265495 a(n) is the smallest k > 0 for which there exists a root quad (-k,x,y,z) such that some bend is first repeated in the n-th generation of descendants (by Descartes reflection).

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%I A265495 #21 Mar 08 2020 03:38:21
%S A265495 1,2,7,6,14,29
%N A265495 a(n) is the smallest k > 0 for which there exists a root quad (-k,x,y,z) such that some bend is first repeated in the n-th generation of descendants (by Descartes reflection).
%C A265495 Perhaps a(0) should be 0, for the quad (0,0,1,1).
%C A265495 Functions were written in the statistical language R to generate root quads and to generate successive generations of descendants. The n-th generation (n >= 1) contains 4*3^(n-1) quads.
%H A265495 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.
%H A265495 R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks and C. H. Yan, <a href="https://doi.org/10.1016/S0022-314X(03)00015-5">Apollonian Circle Packings: Number Theory</a>, J. Number Theory, 100 (2003), 1-45.
%e A265495 For n = 0,1,2,3,4,5, qualifying root quads are (-1,2,2,3), (-2,3,6,7), (-7,12,17,20), (-6,11,14,15), (-14,19,54,55), (-29,55,60,70). E.g., for n=3, the bend 71 appears in both the second and third generations, in the quads (-6,14,35,71) and (-6,11,42,71).
%Y A265495 Cf. A042944, A045864, A261410.
%K A265495 nonn,more
%O A265495 0,2
%A A265495 _Colin Mallows_, Dec 09 2015