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A002161
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Decimal expansion of square root of Pi.
(Formerly M4332 N1814)
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67
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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
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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} ((-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
Also equals the average distance between two points in two dimensions where coordinates are independent normally distributed random variables with mean 0 and variance 1. - Jean-François Alcover, Oct 31 2014, after Steven Finch
Also diameter of a sphere whose surface area equals Pi^2. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Nov 11 2018
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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
Index entries for transcendental numbers
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EXAMPLE
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1.7724538509055160272981674833411451827975494561223871282138...
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MAPLE
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evalf(sqrt(Pi), 120); # Muniru A Asiru, Nov 11 2018
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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)); \\ Harry J. Smith, May 01 2009
(Magma) R:= RealField(100); Sqrt(Pi(R)); // G. C. Greubel, Mar 10 2018
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CROSSREFS
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Cf. A000796, A002388, 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 A255272 A335929
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
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STATUS
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approved
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