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A019669 Decimal expansion of Pi/2. 51
1, 5, 7, 0, 7, 9, 6, 3, 2, 6, 7, 9, 4, 8, 9, 6, 6, 1, 9, 2, 3, 1, 3, 2, 1, 6, 9, 1, 6, 3, 9, 7, 5, 1, 4, 4, 2, 0, 9, 8, 5, 8, 4, 6, 9, 9, 6, 8, 7, 5, 5, 2, 9, 1, 0, 4, 8, 7, 4, 7, 2, 2, 9, 6, 1, 5, 3, 9, 0, 8, 2, 0, 3, 1, 4, 3, 1, 0, 4, 4, 9, 9, 3, 1, 4, 0, 1, 7, 4, 1, 2, 6, 7, 1, 0, 5, 8, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With offset 2, decimal expansion of 5*Pi. - Omar E. Pol, Oct 03 2013

Decimal expansion of the number of radians in a quadrant. - John W. Nicholson, Oct 07 2013

Not the same as A085679. First differing term occurs at 10^-49, as list -49, or 51st counting term (a(-49)= 5 and A085679(-49) = 4). - John W. Nicholson, Oct 07 2013

5*Pi is also the surface area of a sphere whose diameter equals the square root of 5. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Dec 22 2013

Pi/2 is also the radius of a sphere whose surface area equals the volume of the circumscribed cube. - Omar E. Pol, Dec 27 2013

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Johan Wästlund, An Elementary Proof of the Wallis Product Formula for pi, The American Mathematical Monthly 114:10 (Dec. 2007), pp. 914-917.

Eric W. Weisstein and Jonathan Sondow, Wallis Formula, MathWorld.

FORMULA

Pi/2 = log(i)/i, where i = sqrt(-1). - Eric Desbiaux, Jun 27 2009

Pi/2 = Product_{n>=1} (n/(n+1))^((-1)^n)) = 2 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * 8/7 * 8/9 * 10/9 * ... (Wallis formula). - William Keith and Alonso del Arte, Jun 24 2012

Equals Sum_{k>1} 2^k/binomial(2*k,k). [Bruno Berselli, Sep 11 2015]

The previous result is the particular case n = 1 of the more general identity: Pi/2 = 4^(n-1) * n!/(2*n)! * Sum_{k >= 2} 2^(k+1)*(k + n - 1)!*(k + 2*n - 2)!/(2*k + 2*n - 2)! valid for n = 0,1,2,... . - Peter Bala, Oct 26 2016

Pi/2 = Product_{n>=1} (4*n^2)/(4*n^2-1). - Fred Daniel Kline, Oct 29 2016

EXAMPLE

Pi/2 = 1.570796326794896619231321691639751442098584699...

5*Pi = 15.70796326794896619231321691639751442098584699...

MAPLE

Digits:=100: evalf(Pi/2); # Wesley Ivan Hurt, Oct 26 2016

MATHEMATICA

RealDigits[N[Pi/2, 200]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

PROG

(PARI) { default(realprecision, 20080); x=Pi/2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019669.txt", n, " ", d)); } \\ Harry J. Smith, May 31 2009

CROSSREFS

Cf. A053300 (continued fraction).

Cf. A000796, A019692, A122952, A019694 (Pi through 4*Pi).

Sequence in context: A216547 A221208 A085679 * A088394 A021950 A072417

Adjacent sequences:  A019666 A019667 A019668 * A019670 A019671 A019672

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 20 14:50 EDT 2017. Contains 289625 sequences.