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 A004200 Continued fraction for Sum[ 1/3^(2^n),{n,0,Infinity} ]. (Formerly M1312) 13
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217. Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217. FORMULA 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, May 17 2005 EXAMPLE 0.456942562477639661115491826... = 0 + 1/(2 + 1/(5 + 1/(3 + 1/(3 + ...)))). MAPLE 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 # Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Dec 02 2002 MATHEMATICA ContinuedFraction[ NSum[1/3^(2^n), {n, 0, Infinity}, WorkingPrecision -> 105], 105] (* Jean-François Alcover, Jul 18 2011 *) PROG (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])); } \\ Harry J. Smith, May 10 2009 CROSSREFS Cf. A007400, A078885 (decimal expansion). Sequence in context: A287040 A212887 A163766 * A069998 A162405 A141637 Adjacent sequences:  A004197 A004198 A004199 * A004201 A004202 A004203 KEYWORD nonn,cofr AUTHOR EXTENSIONS Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001 STATUS approved

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)