A059444 Decimal expansion of square root of (Pi * e / 2).

2, 0, 6, 6, 3, 6, 5, 6, 7, 7, 0, 6, 1, 2, 4, 6, 4, 6, 9, 2, 3, 4, 6, 9, 5, 9, 4, 2, 1, 4, 9, 9, 2, 6, 3, 2, 4, 7, 2, 2, 7, 6, 0, 9, 5, 8, 4, 9, 5, 6, 5, 4, 2, 2, 5, 7, 7, 8, 3, 2, 5, 6, 2, 6, 8, 9, 8, 9, 7, 8, 9, 6, 4, 2, 5, 6, 7, 0, 8, 5, 1, 6, 1, 8, 1, 2, 6, 0, 1, 8, 1, 2, 2, 7, 7, 3, 3, 1, 4, 1

Offset

1,1

Comments

Appears as constant factor in Proposition 1.12, p. 5, of Feige et al. (2007). - Jonathan Vos Post, Jun 18 2007

References

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.

Links

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

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Uri Feige, Guy Kindler, Ryan O Donnell, Understanding Parallel Repetition Requires Understanding Foams, Electronic Colloquium on Computational Complexity, Report TR07-043 (ISSN 1433-8092, 14th Year, 43rd Report), 7 May 2007.

OEIS Wiki, A remarkable formula of Ramanujan

Formula

Sqrt(Pi*e/2) = A + B with A = 1 + 1/(1*3) + 1/(1*3*5) + 1/(1*3*5*7) + 1/(1*3*5*7*9) + ... = 1.410686134... (see A060196) and B = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4/(1 + 5/(1 + ...)))))) = 0.65567954241... (see A108088) - (S. Ramanujan)

Equals (sqrt(2)*exp(1/4)*(sum(n>=0, n!/(2*n)! ) - 1))/erf(1/2). - Jean-François Alcover, Mar 22 2013

Example

2.066365677...

Mathematica

RealDigits[N[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]][[1]]

Prog

(PARI) { default(realprecision, 20080); x=sqrt(Pi*exp(1)/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b059444.txt", n, " ", d)); } \\ Harry J. Smith, Jun 27 2009

Crossrefs

Cf. A059445, A060196, A108088.

Sequence in context: A296040 A053206 A106848 * A328473 A268656 A318619

Adjacent sequences: A059441 A059442 A059443 * A059445 A059446 A059447

Keyword

nonn,cons

Author

Robert G. Wilson v, Feb 01 2001

Extensions

Edited by Daniel Forgues, Apr 14 2011

Status

approved