

A059444


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


4



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



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 TR07043 (ISSN 14338092, 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).  JeanFrançois 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=(xd)*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



