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A076214
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Decimal expansion of C=sum(k>=0,1/2^(2^k-1)).
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2
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1, 6, 3, 2, 8, 4, 3, 0, 1, 8, 0, 4, 3, 7, 8, 6, 2, 8, 7, 4, 1, 6, 1, 5, 9, 4, 7, 5, 0, 6, 1, 0, 5, 0, 4, 4, 3, 4, 0, 6, 6, 2, 2, 7, 5, 1, 8, 4, 1, 1, 0, 5, 6, 0, 8, 6, 8, 2, 4, 2, 1, 8, 0, 7, 6, 8, 6, 1, 1, 1, 2, 2, 8, 3, 8, 9, 1, 1, 0, 6, 0, 0, 1, 2, 0, 9, 7, 0, 6, 2, 6, 4, 9, 6, 7, 9, 4, 5, 3, 1, 2, 3, 5, 1, 1
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This constant has a nice continued fraction expansion (i.e. only 1 and 2 occur). 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)).
sum(1/2^(2^k - 1), k=0 to infinity) = 2*sum(1/2^(2^k), k=0 to infinity) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,20000
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EXAMPLE
| 1.632843018043786287416159475061050443406622751841105608682421807686111... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
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MATHEMATICA
| Take[ RealDigits[ 2*NSum[1/2^2^k, {k, 0, Infinity}, WorkingPrecision -> 120]][[1]], 105] (* From Jean-François Alcover, Nov 15 2011 *)
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PROG
| (PARI) { default(realprecision, 20080); x=suminf(k=0, 1/2^(2^k)); x*=2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b076214.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
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CROSSREFS
| Cf. A006466 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 09 2009]
Sequence in context: A049605 A088395 A177707 * A011488 A021162 A096840
Adjacent sequences: A076211 A076212 A076213 * A076215 A076216 A076217
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KEYWORD
| cons,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 03 2002
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EXTENSIONS
| Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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