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Search: id:A002937
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| A002937 |
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An exotic continued fraction (for real root of x^3-8x-10).
(Formerly M2284 N0903)
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+0
2
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| 3, 3, 7, 4, 2, 30, 1, 8, 3, 1, 1, 1, 9, 2, 2, 1, 3, 22986, 2, 1, 32, 8, 2, 1, 8, 55, 1, 5, 2, 28, 1, 5, 1, 1501790, 1, 2, 1, 7, 6, 1, 1, 5, 2, 1, 6, 2, 2, 1, 2, 1, 1, 3, 1, 3, 1, 2, 4, 3, 1, 35657
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. M. Stark, An explanation of some exotic continued fractions found by Brillhart, pp. 21-35 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 227.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
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EXAMPLE
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3.318628217750185659109680153... = 3 + 1/(3 + 1/(7 + 1/(4 + 1/(2 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 11 2009]
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PROGRAM
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=NULL; p=x^3 - 8*x - 10; rs=polroots(p); r=real(rs[1]); c=contfrac(r); for (n=1, 20001, write("b002937.txt", n-1, " ", c[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 11 2009]
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CROSSREFS
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Cf. A160332 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 11 2009]
Sequence in context: A156838 A100587 A099282 this_sequence A085870 A096633 A118362
Adjacent sequences: A002934 A002935 A002936 this_sequence A002938 A002939 A002940
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KEYWORD
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cofr,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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