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

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

J. O. Shallit, 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

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]

Adjacent sequences: A006463 A006464 A006465 this_sequence A006467 A006468 A006469

Sequence in context: A072911 A053150 A163379 this_sequence A086597 A031214 A056059

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