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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,...]. - 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

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.