

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,... = A060546.  Jeffrey Shallit, Jun 14 2016


LINKS



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



KEYWORD



AUTHOR



STATUS

approved



