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 A105415 Decimal expansion of the Paris constant. 0
 1, 0, 9, 8, 6, 4, 1, 9, 6, 4, 3, 9, 4, 1, 5, 6, 4, 8, 5, 7, 3, 4, 6, 6, 8, 9, 1, 7, 3, 4, 3, 5, 9, 6, 2, 1, 0, 8, 7, 3, 3, 4, 8, 3, 9, 6, 1, 0, 8, 2, 9, 7, 1, 6, 7, 2, 1, 1, 8, 3, 3, 0, 5, 3, 2, 7, 8, 7, 1, 9, 8, 9, 2, 0, 4, 3, 5, 3, 1, 3, 3, 2, 4, 8, 9, 9, 2, 8, 8, 9, 5, 5, 2, 4, 7, 9, 9, 9, 4, 6, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS T. Piezas III, Golden ratio and nested radicals Simon Plouffe, Generalized expansions of real numbers, 2006 Eric Weisstein's World of Mathematics, Paris Constant EXAMPLE 1.098641964... MATHEMATICA ParisC = Catch[ For[ lastc = 0; c = 1; phi = 1; n = 2, True, n++, phi = N[Sqrt[1 + phi], 110]; c = c*2*GoldenRatio / (GoldenRatio + phi); If[ c - lastc < 10^-105, Throw[c], lastc = c]]]; RealDigits[ ParisC ][[1]][[1 ;; 102]] (* Jean-François Alcover, Oct 26 2012 *) \$MaxExtraPrecision = 1000; Take[RealDigits[SequenceLimit[N[Table[(GoldenRatio - Nest[Sqrt[1 + #] &, 0, n]) (2 GoldenRatio)^n / 2, {n, 200}], 300]]][[1]], 200] (* Vladimir Reshetnikov, Nov 18 2015 *) CROSSREFS Cf. A001622. Sequence in context: A087044 A246168 A248585 * A197015 A239387 A226735 Adjacent sequences:  A105412 A105413 A105414 * A105416 A105417 A105418 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Apr 05 2005 STATUS approved

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Last modified November 14 23:25 EST 2018. Contains 317221 sequences. (Running on oeis4.)