A006467 Continued fraction for Sum_{n>=0} (-1)^n/3^(2^n). (Formerly M3206)

0, 4, 3, 1, 3, 5, 1, 3, 5, 3, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 3, 5, 1, 3, 3, 5, 3, 1, 5, 3, 1, 3, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 3, 1, 5, 3, 1, 3, 5, 3, 3, 1, 3, 5, 1, 3, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 3, 5, 1, 3, 5, 3, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 3, 5, 1, 3, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 3, 5, 1, 3, 5

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

J. Shallit, Letter to N. J. A. Sloane with attachment, Aug. 1979

Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217 [DOI]

Example

0.234415508674864614413415474... = 0 + 1/(4 + 1/(3 + 1/(1 + 1/(3 + ...)))). - Harry J. Smith, May 12 2009

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[2], Buv[3][n]+(-1)^Buv[2], seq(Buv[3][n-i], i=1..n-2)]] od:seq(Buv[3][i], i=1..2^v); # first 2^v terms of A006467 # Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Dec 02 2002

Prog

(PARI) { allocatemem(932245000); default(realprecision, 20000); x=suminf(n=0, (-1)^n/3^(2^n)); x=contfrac(x); for (n=1, 20001, write("b006467.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 12 2009

Crossrefs

Cf. A160386 (decimal expansion). - Harry J. Smith, May 12 2009

Sequence in context: A123683 A010306 A197700 * A119505 A201518 A168616

Adjacent sequences: A006464 A006465 A006466 * A006468 A006469 A006470

Keyword

nonn,cofr

Author

N. J. A. Sloane

Extensions

Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001

Status

approved