A178647 Decimal expansion of the fraction of a population falling within +- 1 standard deviation of the mean, assuming a normal distribution.

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

Offset

0,1

References

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 40, table 40:7:1 at page 387.

Links

Rick L. Shepherd, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Erf.

Wikipedia, 68-95-99.7 rule.

Formula

Equals erf(1/sqrt(2)). - Jean-François Alcover, May 29 2013

Example

0.6826894921370858971704650912640758449558259334532087819747889004859...

Maple

erf(1/sqrt(2)) ; evalf(%) ; # R. J. Mathar, Mar 22 2016

Mathematica

RealDigits[(1 + Erf[1/Sqrt@2])/2 - (1 + Erf[ -1/Sqrt@2])/2, 10, 111][[1]] (* Robert G. Wilson v, Jun 01 2010 *)

Prog

(MATLAB) 0.5*(1+erf(1/sqrt(2)))- 0.5*(1+erf(-1/sqrt(2)))
(PARI) (erfc(-1/sqrt(2))-erfc(1/sqrt(2)))/2 \\ Charles R Greathouse IV, Sep 04 2012
(PARI) 1 - erfc(1/sqrt(2)) \\ Rick L. Shepherd, Mar 05 2014

Crossrefs

Cf. A110894 (2sigma), A270712 (3sigma).

Sequence in context: A362976 A154564 A152914 * A093204 A365823 A054512

Adjacent sequences: A178644 A178645 A178646 * A178648 A178649 A178650

Keyword

nonn,cons

Author

Joost de Winter, May 31 2010

Extensions

More terms from Robert G. Wilson v, Jun 01 2010

Edited by N. J. A. Sloane, Jun 07 2010

Status

approved