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A007400 Continued fraction for sum(n>=0, 1/2^(2^n) ) = 0.8164215090218931... 18
0, 1, 4, 2, 4, 4, 6, 4, 2, 4, 6, 2, 4, 6, 4, 4, 2, 4, 6, 2, 4, 4, 6, 4, 2, 6, 4, 2, 4, 6, 4, 4, 2, 4, 6, 2, 4, 4, 6, 4, 2, 4, 6, 2, 4, 6, 4, 4, 2, 6, 4, 2, 4, 4, 6, 4, 2, 6, 4, 2, 4, 6, 4, 4, 2, 4, 6, 2, 4, 4, 6, 4, 2, 4, 6, 2, 4, 6, 4, 4, 2, 4, 6, 2, 4, 4, 6, 4, 2, 6, 4, 2, 4, 6, 4, 4, 2, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

H. Cohn, Symmetry and specializability in continued fractions

Jeffrey 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

FORMULA

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, May 17 2005

EXAMPLE

0.816421509021893143708079737... = 0 + 1/(1 + 1/(4 + 1/(2 + 1/(4 + ...))))

MATHEMATICA

a[n_] := a[n] = Which[n < 3, {0, 1, 4}[[n+1]], Mod[n, 8] == 1, a[(n+1)/2], Mod[n, 8] == 2, a[(n+2)/2], True, {2, 0, 0, 2, 4, 4, 6, 4, 2, 0, 0, 2, 4, 6, 4, 4}[[Mod[n, 16]+1]]]; Table[a[n], {n, 0, 98}] (* Jean-François Alcover, Nov 29 2013, after Ralf Stephan *)

PROG

(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]))) /* Ralf 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])); } \\ Harry J. Smith, May 07 2009

CROSSREFS

Cf. A007404, A089267.

Sequence in context: A179411 A103859 A253808 * A057696 A057697 A019921

Adjacent sequences:  A007397 A007398 A007399 * A007401 A007402 A007403

KEYWORD

nonn,cofr

AUTHOR

Simon Plouffe, Jeffrey Shallit

STATUS

approved

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Last modified August 29 01:49 EDT 2015. Contains 261184 sequences.