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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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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 227.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (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.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,20000
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EXAMPLE
| 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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PROG
| (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
| Cf. A160332 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 11 2009]
Sequence in context: A100587 A187419 A099282 * A085870 A096633 A175482
Adjacent sequences: A002934 A002935 A002936 * A002938 A002939 A002940
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KEYWORD
| cofr,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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