login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006467 Continued fraction for Sum_{n>=0} (-1)^n/3^(2^n).
(Formerly M3206)
2
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 (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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 23:17 EST 2020. Contains 332319 sequences. (Running on oeis4.)