0,5

C arises when looking for a sequence b(n) such that : b(1)=0, b(n+1) is the smallest integer > b(n) such that the continued fraction for 1/2^b(1)+1/2^b(2)+...+1/2^b(n+1) contains only 1's or 2's. Because b(n)=2^n-1 and C = sum(k>=0,1/2^b(k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 03 2002

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

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

Recurrence: a(5n)=a(5n+1)=a(2)=a(5n+3)=a(20n+14)=a(40n+9)=1, a(20n+4)=a(40n+29)=2, a(5n+2)=3-a(5n-1), a(20n+19)=a(10n+9). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 17 2005

1.632843018043786287416159475... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]

(PARI) { allocatemem(932245000); default(realprecision, 10000); x=suminf(n=0, 1/2^(2^n)); x=contfrac(2*x); for (n=1, 20001, write("b006466.txt", n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]

Cf. A076214 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]

Sequence in context: A072911 A053150 A163379 this_sequence A086597 A031214 A056059

Adjacent sequences: A006463 A006464 A006465 this_sequence A006467 A006468 A006469

nonn,cofr

N. J. A. Sloane (njas(AT)research.att.com).

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