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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
15
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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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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).
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.
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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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