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Search: id:A048652
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| A048652 |
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Continued fraction for Product_{k >= 1} (1-1/2^k) (Cf. A048651). |
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+0
5
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| 0, 3, 2, 6, 4, 1, 2, 1, 9, 2, 1, 2, 3, 2, 3, 5, 1, 2, 1, 1, 6, 1, 2, 5, 79, 6, 4, 5, 1, 1, 1, 1, 12, 1, 1, 2, 5, 1, 659, 2, 17, 1, 5, 2, 3, 2, 6, 1, 1, 2, 3, 1, 2, 6, 1, 1, 3, 11, 1, 1, 2, 1, 1, 2, 4, 11, 2, 1, 3, 4, 2, 2, 1, 3, 1, 71, 1, 1, 1, 19, 1, 4, 1, 1, 8, 1, 49, 3, 1, 2, 2, 11, 1, 11, 10, 1, 2, 1, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Continued fraction expansion of the constant Product{k=1..inf} (1-1/2^k)^(-1) = 3.46274661945506361... (A065446) gives essentially the same sequence.
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
S. R. Finch, Digital Search Tree Constants
G. Xiao, Contfrac
Index entries for continued fractions for constants
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EXAMPLE
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0.2887880950866024212788997219294585937270...
0.288788095086602421278899721... = 0 + 1/(3 + 1/(2 + 1/(6 + 1/(4 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 02 2009]
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MATHEMATICA
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ContinuedFraction[ N[ Product[ 1/(1 - 1/2^k), {k, 1, Infinity} ], 500 ], 49]
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PROGRAM
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=prodinf(k=1, -1/2^k, 1); z=contfrac(x); for (n=1, 20001, write("b048652.txt", n-1, " ", z[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 07 2009]
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CROSSREFS
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Cf. A005329, A048651, A065446.
Sequence in context: A064455 A141619 A065021 this_sequence A057050 A123042 A121647
Adjacent sequences: A048649 A048650 A048651 this_sequence A048653 A048654 A048655
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KEYWORD
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nonn,cofr
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected by Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 02 2009
Deleted old PARI program Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 20 2009
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