0,3

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

Harry J. Smith, Table of n, a(n) for n=0,...,20000

H. Cohn, Symmetry and specializability in continued fractions

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

A. J. van der Poorten, An introduction to continued fractions

G. Xiao, Contfrac

Index entries for continued fractions for constants

Recurrence: a(0)=0, a(1)=1, a(2)=4, a(8n)=a(8n+3)=2, a(8n+4)=a(8n+7)=a(16n+5)=a(16n+14)=4, a(16n+6)=a(16n+13)=6, a(8n+1)=a(4n+1), a(8n+2)=a(4n+2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 17 2005

0.816421509021893143708079737... = 0 + 1/(1 + 1/(4 + 1/(2 + 1/(4 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 01 2009]

(PARI) a(n)=if(n<3, [0, 1, 4][n+1], if(n%8==1, a((n+1)/2), if(n%8==2, a((n+2)/2), [2, 0, 0, 2, 4, 4, 6, 4, 2, 0, 0, 2, 4, 6, 4, 4][(n%16)+1]))) /* from R. Stephan */

(PARI) a(n)=contfrac(suminf(n=0, 1/2^(2^n)))[n+1]

(PARI) { allocatemem(932245000); default(realprecision, 26000); x=suminf(n=0, 1/2^(2^n)); x=contfrac(x); for (n=1, 20001, write("b007400.txt", n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 07 2009]

Cf. A007404.

Cf. A089267.

Sequence in context: A095382 A135282 A103859 this_sequence A019921 A061469 A021706

Adjacent sequences: A007397 A007398 A007399 this_sequence A007401 A007402 A007403

nonn,cofr

Simon Plouffe (simon.plouffe(AT)gmail.com), Jeff Shallit (shallit(AT)graceland.uwaterloo.ca)

Deleted old PARI program Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 20 2009