

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^(i1).


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
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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,...].  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+...))))).


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.
Cf. Blazys's continued fractions: A233588, A233589, A233591 and Blazys' expansions: A233582, A233583, A233584, A233585, A233586, A233587
Sequence in context: A245174 A109169 A011291 * A078889 A176534 A154847
Adjacent sequences: A233587 A233588 A233589 * A233591 A233592 A233593


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Jan 06 2014


STATUS

approved



