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 A270137 Decimal expansion of the constant 6/A270121(1) + Sum_{n>=2} 1/A270121(n). 0
 0, 8, 6, 6, 0, 7, 3, 9, 0, 8, 7, 3, 0, 1, 5, 9, 2, 9, 9, 7, 1, 2, 6, 4, 1, 4, 0, 6, 8, 5, 8, 4, 8, 0, 6, 4, 2, 8, 6, 6, 3, 1, 1, 5, 2, 3, 8, 6, 2, 7, 3, 2, 1, 1, 6, 0, 0, 9, 7, 3, 3, 8, 6, 5, 9, 3, 2, 8, 1, 9, 3, 5, 3, 8, 1, 8, 9, 1, 4, 0, 6, 7, 4, 4, 5, 4, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A270121 is defined by the following recurrence: if A270121(n)=x(n) then x(n+1)*x(n-1)=x(n)^2*(1+n*x(n)) for n>=1, with x(1)=7, x(2)=112; and for A270124, if A270124(n)=y(n) then y(0)=2 and y(n)=x(n+1)/x(n) for n>=1. Both of these sequences appear in the continued fraction expansion of this number, which is transcendental. LINKS A. N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.4. A. N. W. Hone, Continued fractions for some transcendental numbers, arXiv:1509.05019 [math.NT], 2015-2016, Monatsh. Math. DOI: 10.1007/s00605-015-0844-2. FORMULA The continued fraction expansion takes the form [0; 1, 6, A270124(0), A270121(1), ..., n*A270124(n-1), A270121(n), (n+1)*A270124(n), A270121(n+1), ...]. EXAMPLE 0.86607390873015929971... = 6/A270121(1) + Sum_{n>=2} 1/A270121(n) = 6/7 + 1/112 + 1/403200 + 1/1755760043520000 + ... = [0; 1, 6, 2, 7, 32, 112, 10800, 403200, 17418254400, ...] = [0; 1, 6, A270124(0), A270121(1), 2*A270124(1), A270121(2), 3*A270124(2), A270121(3), 4*A270124(3), ...] (continued fraction). CROSSREFS Cf. A112373, A114550, A114551, A114552. Sequence in context: A046266 A165104 A010527 * A269846 A316136 A102887 Adjacent sequences:  A270134 A270135 A270136 * A270138 A270139 A270140 KEYWORD nonn,cons AUTHOR Andrew Hone, Mar 11 2016 EXTENSIONS More terms from Jon E. Schoenfield, Nov 12 2016 STATUS approved

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Last modified January 20 14:26 EST 2020. Contains 331094 sequences. (Running on oeis4.)