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Search: id:A002163
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| A002163 |
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Decimal expansion of square root of 5.
(Formerly M0293 N0105)
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+0
17
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| 2, 2, 3, 6, 0, 6, 7, 9, 7, 7, 4, 9, 9, 7, 8, 9, 6, 9, 6, 4, 0, 9, 1, 7, 3, 6, 6, 8, 7, 3, 1, 2, 7, 6, 2, 3, 5, 4, 4, 0, 6, 1, 8, 3, 5, 9, 6, 1, 1, 5, 2, 5, 7, 2, 4, 2, 7, 0, 8, 9, 7, 2, 4, 5, 4, 1, 0, 5, 2, 0, 9, 2, 5, 6, 3, 7, 8, 0, 4, 8, 9, 9, 4, 1, 4, 4, 1, 4, 4, 0, 8, 3, 7, 8, 7, 8, 2, 2, 7
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the limiting ratio of Lucas[n]/Fibonacci[n]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 10 2007
Continued fraction expansion is 2 followed by {4} repeated. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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REFERENCES
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M. F. Jones, 22900D approximations to the square roots of the primes less than 100, Math. Comp., 22 (1968), 234-235.
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 106.
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).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
D. Merrill, First million digits of square root of 5
R. Nemiroff and J. Bonnell, The first 1 million digits of the square root of 5
R. Nemiroff and J. Bonnell, Plouffe's Inverter, The first 1 million digits of the square root of 5
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
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e^(i*Pi)+ 2*Phi = sqrt(5).
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EXAMPLE
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2.236067977499789696409173668731276235440618359611525724270897245410520... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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PROGRAM
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(PARI) { default(realprecision, 20080); x=sqrt(5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002163.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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CROSSREFS
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Cf. A000032, A000045.
Cf. A040002 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
Sequence in context: A080669 A099205 A051005 this_sequence A093422 A083506 A076333
Adjacent sequences: A002160 A002161 A002162 this_sequence A002164 A002165 A002166
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Sequence corrected by Paul Zimmermann Mar 15, 1996. Additional comments from Jason Earls (zevi_35711(AT)yahoo.com), Mar 26 2001.
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