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 A210395 Decimal expansion of continued fraction with quotients equal to Fermat numbers. 0
 3, 1, 9, 7, 6, 7, 4, 9, 4, 4, 5, 8, 7, 6, 5, 5, 9, 3, 6, 4, 1, 1, 6, 2, 8, 9, 0, 2, 1, 7, 5, 2, 4, 4, 8, 0, 2, 1, 2, 7, 8, 3, 5, 2, 5, 4, 1, 4, 9, 1, 5, 7, 1, 9, 2, 5, 7, 5, 1, 4, 9, 3, 1, 6, 9, 9, 2, 9, 2, 8, 9, 3, 2, 1, 5, 9, 9, 2, 6, 8, 0, 0, 7, 9, 9, 5, 5, 7, 8, 7, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES A. Ya. Khinchin, Continued Fractions, Dover Publications, 1997. M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, Springer, 2011. LINKS Wikipedia, Continued fraction Wikipedia, Fermat number FORMULA a(0).a(1)a(2)a(3)a(4)a(5)... = F_0 + 1/(F_1 + 1/(F_2 + 1/(F_3 + 1/(F_4 + ...)))) = [F_0,F_1,F_2,F_3,F_4,...] where a(0).a(1)a(2)a(3)a(4)... is a decimal representation of the continued fraction [F_0,F_1,F_2,F_3,F_4,...] where F_0, F_1,... are Fermat numbers. EXAMPLE 3.19767494... = 3 + 1/(5 + 1/(17 + 1/(257 + 1/(65537 + ...)))) MATHEMATICA FromContinuedFraction[{3, 5, 17, 257, 65537, 4294967297, 18446744073709551617}] (* for better precision, enter next Fermat numbers *) PROG (PARI) s=3; forstep(n=log(default(realprecision)*log(10)\log(2))\log(2), 1, -1, s=1/(2.^(2^n)+s+1)); s \\ Charles R Greathouse IV, Mar 21 2012 CROSSREFS Cf. A000215. Sequence in context: A143495 A327997 A245789 * A019770 A136320 A201840 Adjacent sequences:  A210392 A210393 A210394 * A210396 A210397 A210398 KEYWORD nonn,cons AUTHOR Algirdas Javtokas, Mar 21 2012 EXTENSIONS Offset changed by Bruno Berselli, May 14 2012 STATUS approved

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Last modified May 31 04:43 EDT 2020. Contains 334747 sequences. (Running on oeis4.)