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A152416 Decimal expansion of 2 - Pi^2/6. 2
3, 5, 5, 0, 6, 5, 9, 3, 3, 1, 5, 1, 7, 7, 3, 5, 6, 3, 5, 2, 7, 5, 8, 4, 8, 3, 3, 3, 5, 3, 9, 7, 4, 8, 1, 0, 7, 8, 1, 0, 5, 0, 0, 9, 8, 7, 9, 3, 2, 0, 1, 5, 6, 2, 2, 6, 4, 4, 4, 1, 7, 7, 0, 6, 2, 9, 9, 9, 2, 5, 2, 9, 5, 9, 6, 7, 9, 9, 1, 2, 6, 1, 6, 6, 3, 7, 1, 0, 9, 9, 3, 8, 0, 2, 4, 1, 2, 9, 4, 6, 9, 5, 9, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Essentially the 9's complement of the digits of A013661, starting with the second. Consider the constants N(s) = Sum_{n >= 2} 1/(n^s*(n-1)) = s - Sum_{k=2..s} Zeta(k), where Zeta is Riemann's zeta function. N(1)=1 and this constant here is N(2).

The proportion of triangles formed by random lines in a plane (see Theorem 6 in Miles link). - Michel Marcus, Sep 04 2015

LINKS

Table of n, a(n) for n=0..104.

Mathematical Reflections, Solution to Problem U268, Issue 3, 2013, p 17.

R. E. Miles, Random polygons determined by random lines in a plane, PNAS 1964 52 (4) 901-907.

FORMULA

Equals 2 - A013661.

Equals lim_{n->oo} (1/n^2)*Sum_{k=2..n^2-1} (fractional_part(n/sqrt(k))). See Mathematical Reflections link. - Michel Marcus, Jan 06 2017

EXAMPLE

Equals 0.355065933151773563527584833353974810781050098793201562264441770...

MAPLE

evalf(2-Pi^2/6);

MATHEMATICA

First@ RealDigits[N[2 - Pi^2/6, 120]] (* Michael De Vlieger, Sep 04 2015 *)

PROG

(PARI) 2 - Pi^2/6 \\ Michel Marcus, Jan 06 2017

CROSSREFS

Cf. A013661.

Sequence in context: A242288 A021742 A284867 * A200334 A138112 A106233

Adjacent sequences:  A152413 A152414 A152415 * A152417 A152418 A152419

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Dec 03 2008

STATUS

approved

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Last modified July 22 11:00 EDT 2019. Contains 325219 sequences. (Running on oeis4.)