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A002161
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Decimal expansion of square root of Pi.
(Formerly M4332 N1814)
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37
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1, 7, 7, 2, 4, 5, 3, 8, 5, 0, 9, 0, 5, 5, 1, 6, 0, 2, 7, 2, 9, 8, 1, 6, 7, 4, 8, 3, 3, 4, 1, 1, 4, 5, 1, 8, 2, 7, 9, 7, 5, 4, 9, 4, 5, 6, 1, 2, 2, 3, 8, 7, 1, 2, 8, 2, 1, 3, 8, 0, 7, 7, 8, 9, 8, 5, 2, 9, 1, 1, 2, 8, 4, 5, 9, 1, 0, 3, 2, 1, 8, 1, 3, 7, 4, 9, 5, 0, 6, 5, 6, 7, 3, 8, 5, 4, 4, 6, 6, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Also Gamma(1/2). - Franklin T. Adams-Watters, Apr 07 2006
The integral of the Gaussian function Exp(-x^2) over the real line. - Richard Chapling (r.chappers(AT)gmail.com), Jun 05 2008
sqrt(Pi) = 1/2*sum_{n=0..infinity} ((-1)^n * (4*n+1) * (1/8)^(n+1) * (2^(n+1))^3 * GAMMA(n+1/2)^3 / GAMMA(n+1)^3). - Alexander R. Povolotsky, Mar 25 2013
Also equals integral_{x=0..1} 1/sqrt(-log(x)). [Jean-François Alcover, Apr 29 2013]
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REFERENCES
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George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 190.
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
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
Donald Knuth, Why pi?, Christmas Tree lecture, Dec 06 2010 (video)
Index entries for sequences related to the number Pi
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EXAMPLE
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1.7724538509055160272981674833411451827975494561223871282138...
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MATHEMATICA
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RealDigits[N[Sqrt[Pi], 120]][[1]] - Richard Chapling (r.chappers(AT)gmail.com), Jun 05 2008
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PROG
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(PARI) { default(realprecision, 20080); x=sqrt(Pi); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002161.txt", n, " ", d)); } [From Harry J. Smith, May 01 2009]
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CROSSREFS
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Cf. A000796, A073006, A195907, A203145.
Cf. decimal expansions of Gamma(1/k): A073005 (k=3), A068466 (k=4), A175380 (k=5), A175379 (k=6), A220086 (k=7), A203142 (k=8).
Sequence in context: A102400 A144860 A113810 * A083871 A169812 A195907
Adjacent sequences: A002158 A002159 A002160 * A002162 A002163 A002164
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Franklin T. Adams-Watters, Apr 07 2006
Fixed my PARI program, had -n Harry J. Smith, May 19 2009
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STATUS
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approved
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