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A006083
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Continued fraction for e/2.
(Formerly M0125)
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4
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1, 2, 1, 3, 1, 1, 1, 3, 3, 3, 1, 3, 1, 3, 5, 3, 1, 5, 1, 3, 7, 3, 1, 7, 1, 3, 9, 3, 1, 9, 1, 3, 11, 3, 1, 11, 1, 3, 13, 3, 1, 13, 1, 3, 15, 3, 1, 15, 1, 3, 17, 3, 1, 17, 1, 3, 19, 3, 1, 19, 1, 3, 21, 3, 1, 21, 1, 3, 23, 3, 1, 23, 1, 3, 25, 3, 1, 25, 1, 3, 27, 3, 1, 27, 1, 3, 29, 3, 1, 29, 1, 3, 31, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 601.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
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FORMULA
| a(1)=1, a(2)=2, a(3)=1, a(4)=3, a(5)=1, a(6)=1, a(7)=1, a(8)=3, then for k>=1 a(6k+3)=a(6k+6)=2k+1, a(6k+4)=a(6k+8)=3, a(6k+5)=a(6k+7)=1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 08 2003
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EXAMPLE
| 1.359140914229522617680143735... = 1 + 1/(2 + 1/(1 + 1/(3 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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MATHEMATICA
| ContinuedFraction[E/2, 94] (* From Jean-François Alcover, Apr 1 2011 *)
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 55000); x=contfrac(exp(1)/2); for (n=1, 20000, write("b006083.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
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CROSSREFS
| Cf. A019739 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 10 2009]
Sequence in context: A125168 A051794 A110969 * A080301 A057021 A152443
Adjacent sequences: A006080 A006081 A006082 * A006084 A006085 A006086
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KEYWORD
| cofr,nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003
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