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

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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

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

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]

Crossrefs

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

Programs

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

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

Extensions

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