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A006084
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Continued fraction for e/3.
(Formerly M4591)
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4
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0, 1, 9, 1, 1, 1, 5, 1, 1, 1, 1, 26, 1, 1, 3, 5, 1, 3, 1, 1, 44, 1, 1, 5, 5, 1, 5, 1, 1, 62, 1, 1, 7, 5, 1, 7, 1, 1, 80, 1, 1, 9, 5, 1, 9, 1, 1, 98, 1, 1, 11, 5, 1, 11, 1, 1, 116, 1, 1, 13, 5, 1, 13, 1, 1, 134, 1, 1, 15, 5, 1, 15, 1, 1, 152, 1, 1, 17, 5, 1, 17, 1, 1, 170, 1, 1, 19, 5, 1, 19, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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
| First eight terms are 0, 1, 9, 1, 1, 1, 5, 1; then a(9k)=2k-1, a(9k+1)=1, a(9k+2)=1, a(9k+3)=18k+8, a(9k+4)=1, a(9k+5)=1, a(9k+6)=2k+1, a(9k+7)=5, a(9k+8)=1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 08 2003
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EXAMPLE
| 0.906093942819681745120095823... = 0 + 1/(1 + 1/(9 + 1/(1 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 12 2009]
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 54000); x=contfrac(exp(1)/3); for (n=1, 20000, write("b006084.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 12 2009]
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CROSSREFS
| Cf. A019740 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 12 2009]
Sequence in context: A087968 A110483 A010164 * A059928 A180839 A010163
Adjacent sequences: A006081 A006082 A006083 * A006085 A006086 A006087
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KEYWORD
| nonn,cofr,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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