id:A045506 - OEIS Search Results

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Inscribe 2 spheres of curvature 2 inside sphere of curvature -1, continue to inscribe spheres where possible; sequence gives list of curvatures.

+0
5

-1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`A 3-dimensional Apollonian (or Soddy) problem.` `Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 11 2008): Appears to coincide with a(n)=2+3*floor((n-1)/2)+(1+(-1)^n)/2-0^n, in which case the g.f. is (-1+3x+2x^2-x^3)/((1+x)(1-x)^2).`
	FORMULA	`Appears to be congruent to 0 or 2 mod 3.`
	CROSSREFS	`Cf. A042944.` `Adjacent sequences: A045503 A045504 A045505 this_sequence A045507 A045508 A045509` `Sequence in context: A030704 A061054 A061723 this_sequence A007494 A052490 A117672`
	KEYWORD	`sign,nice,new`
	AUTHOR	`Brian L. Galebach (sequence(AT)ProbabilitySports.com)`

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Last modified October 9 14:06 EDT 2008. Contains 144831 sequences.

AT&T Labs Research