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Search: id:A004200
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| A004200 |
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Continued fraction for Sum[ 1/3^(2^n),{n,0,Infinity} ].
(Formerly M1312)
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+0
12
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| 0, 2, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 1, 3, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 1, 3, 5, 3, 3, 1, 3, 5, 3
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Shallit, Jeffrey; Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
J. O. Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217.
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FORMULA
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Recurrence: a(0)=0, a(1)=2, a(2)=5, a(16n+5)=a(16n+12)=a(32n+9)=a(32n+24)=1, a(8n+3)=a(8n+6)=a(16n+4)=a(16n+13)=a(32n+8)=a(32n+25)=3, a(8n+2)=a(8n+7)=5, a(16n)=a(8n), a(16n+1)=a(8n+1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 17 2005
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EXAMPLE
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0.456942562477639661115491826... = 0 + 1/(2 + 1/(5 + 1/(3 + 1/(3 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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MAPLE
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u := 3: v := 7: Buv := [u, 1, [0, u-1, u+1]]: for k from 2 to v do n := nops(Buv[3]): Buv := [u, Buv[2]+1, [seq(Buv[3][i], i=1..n-1), Buv[3][n]+1, Buv[3][n]-1, seq(Buv[3][n-i], i=1..n-2)]] od: seq(Buv[3][i], i=1..2^v); # first 2^v terms of A004200
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PROGRAM
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(PARI) { allocatemem(932245000); default(realprecision, 20000); x=suminf(n=0, 1/3^(2^n)); x=contfrac(x); for (n=1, 20001, write("b004200.txt", n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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CROSSREFS
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Cf. A007400.
Cf. A078885 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
Sequence in context: A130848 A156637 A163766 this_sequence A069998 A162405 A141637
Adjacent sequences: A004197 A004198 A004199 this_sequence A004201 A004202 A004203
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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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Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001
Maple program from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Dec 02 2002
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