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 A086744 Decimal expansion of Product_{n>=1} (2n/(2n+1))^((-1)^t(n)), where t(n) = A010060(n) is the Thue-Morse sequence. 5
 1, 6, 2, 8, 1, 6, 0, 1, 2, 9, 7, 1, 8, 9, 1, 7, 2, 4, 8, 8, 2, 1, 5, 3, 1, 2, 2, 5, 4, 0, 9, 9, 7, 3, 2, 3, 4, 9, 9, 5, 1, 5, 5, 7, 5, 9, 2, 6, 9, 7, 7, 7, 6, 5, 4, 1, 6, 1, 6, 2, 7, 9, 7, 4, 6, 8, 9, 9, 0, 7, 9, 1, 1, 3, 1, 5, 7, 6, 7, 9, 1, 6, 1, 6, 7, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It is an open problem to decide if this number is algebraic. The sequence of partial products P_k = Product_{n=1..2^k-1} (2n/(2n+1))^((-1)^t(n)) converges rapidly to the limit as k increases; e.g., P_28 is correct to more than 100 decimal digits. - Jon E. Schoenfield, Aug 17 2014 REFERENCES J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 207. J. Shallit, Number theory and formal languages, in Emerging applications of number theory (Minneapolis, MN, 1996), 547-570, IMA Vol. Math. Appl., 109, Springer, New York, 1999. LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..100 EXAMPLE 1.6281601297189... MATHEMATICA kmax = 28; digits = 100; p[k_] := p[k] = Product[(2n/(2n+1))^(-1)^ThueMorse[n] // N[#, digits+10]&, {n, 2^(k-1), 2^k-1}]; RealDigits[Product[Print["p(", k, ") = ", p[k]]; p[k], {k, 1, kmax}], 10, digits][[1]] (* Jean-François Alcover, Apr 18 2018, after Jon E. Schoenfield's comments *) CROSSREFS Sequence in context: A021090 A270138 A177889 * A242301 A256129 A019692 Adjacent sequences:  A086741 A086742 A086743 * A086745 A086746 A086747 KEYWORD nonn,cons AUTHOR N. J. A. Sloane, Sep 12 2003 EXTENSIONS More terms from Vaclav Kotesovec, Jul 28 2013 More terms from Jon E. Schoenfield, Aug 17 2014 STATUS approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)