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 A233590 Decimal expansion of the continued fraction c(1) +c(1)/(c(2) +c(2)/(c(3) +c(3)/(c(4) +c(4)/....))), where c(i)=2^(i-1). 10
 1, 4, 0, 8, 6, 1, 5, 9, 7, 9, 7, 3, 5, 0, 0, 5, 2, 0, 5, 1, 3, 2, 3, 6, 2, 5, 9, 0, 2, 5, 5, 7, 9, 5, 2, 0, 9, 4, 8, 4, 5, 6, 3, 3, 7, 3, 6, 8, 6, 8, 8, 8, 3, 5, 3, 7, 0, 3, 9, 2, 7, 0, 2, 2, 3, 7, 9, 7, 5, 9, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For more details about this type of continued fraction, see A233588. This one corresponds to the powers of two sequence. Corresponds to the regular continued fraction 1,2,2,4,4,8,8,16,16,... = A060546. - Jeffrey Shallit, Jun 14 2016 LINKS Stanislav Sykora, Table of n, a(n) for n = 1..20000 S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001 S. Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki FORMULA Equals 1+1/(2+2/(4+4/(8+8/(16+16/(32+...))))). Equals Product_{k>=0} ((1 - 2^(5*k + 2))*(1 - 2^(5*k + 3)))/((1 - 2^(5*k + 1))*(1 - 2^(5*k + 4))). - Antonio Graciá Llorente, Mar 20 2024 EXAMPLE 1.408615979735005205132362590255795209484563373686888353703927022... MATHEMATICA RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ (2^Range[0, 27])], 10, 111][[1]] (* Robert G. Wilson v, May 22 2014 *) PROG (PARI) See the link CROSSREFS Cf. A000079 (2^n), A096658, A060546. Cf. Blazys's continued fractions: A233588, A233589, A233591 and Blazys' expansions: A233582, A233583, A233584, A233585, A233586, A233587 Sequence in context: A109169 A011291 A338670 * A078889 A176534 A154847 Adjacent sequences: A233587 A233588 A233589 * A233591 A233592 A233593 KEYWORD nonn,cons AUTHOR Stanislav Sykora, Jan 06 2014 STATUS approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)