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 A248938 Decimal expansion of beta = G^2*(2/3)*Product_{prime p == 3 (mod 4)} (1 - 2/(p*(p-1)^2)) (where G is Catalan's constant), a constant related to the problem of integral Apollonian circle packings. 2
 4, 6, 1, 2, 6, 0, 9, 0, 8, 6, 1, 3, 8, 6, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Steven R. Finch, Apollonian circles with integer curvatures, p. 6. [Cached copy, with permission of the author] Elena Fuchs and Katherine Sanden, Some experiments with integral Apollonian circle packings, arXiv:1001.1406 [math.NT] p. 7. Peter Sarnak, Integral Apollonian Packings, Princeton MAA Lecture - January, 2009, p. 21. FORMULA beta = (G^2/3)*A248930, where G is Catalan's constant A006752. EXAMPLE 0.4612609086138613... MATHEMATICA kmax = 25; Clear[P]; Do[P[k] = Product[p = Prime[n]; If[Mod[p, 4] == 3 , 1 - 2/(p*(p - 1)^2) // N[#, 40]&, 1], {n, 1, 2^k}]; Print["P(", k, ") = ", P[k]], {k, 10, kmax}]; beta = Catalan^2*(2/3)*P[kmax]; RealDigits[beta, 10, 16] // First CROSSREFS Cf. A006752, A042944, A042946, A052483, A189226, A189227, A248930. Sequence in context: A154748 A190282 A164833 * A106144 A154478 A255695 Adjacent sequences:  A248935 A248936 A248937 * A248939 A248940 A248941 KEYWORD nonn,cons,more AUTHOR Jean-François Alcover, Oct 17 2014 STATUS approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)