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A002161 Decimal expansion of square root of Pi.
(Formerly M4332 N1814)
40
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)
OFFSET

1,2

COMMENTS

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

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

REFERENCES

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).

LINKS

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

EXAMPLE

1.7724538509055160272981674833411451827975494561223871282138...

MATHEMATICA

RealDigits[N[Sqrt[Pi], 120]][[1]] (* Richard Chapling (r.chappers(AT)gmail.com), Jun 05 2008 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Franklin T. Adams-Watters, Apr 07 2006

STATUS

approved

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Last modified November 27 15:44 EST 2014. Contains 250224 sequences.