A354238 Decimal expansion of 1 - Pi^2/12.

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

Offset

0,2

Comments

Ratio of area between the polygon that is adjacent in the same plane to the base of the stepped pyramid with an infinite number of levels described in A245092 and the circumscribed square (see the first formula).

Links

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

Ovidiu Furdui, Problem 1930, Mathematics Magazine, Vol. 86, No. 4 (2013), p. 289; A zeta series, Solution to Problem 1930 by Omran Kouba, ibid., Vol. 87, No. 4 (2014), pp. 296-298.

Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (C7.4)

Index entries for transcendental numbers.

Formula

Equals lim_{n->infinity} A004125(n)/(n^2).

Equals 1 - A013661/2.

Equals 1 - A072691.

Equals A152416/2.

Equals Sum_{k>=1} 1/(2*k*(k+1)^2). - Amiram Eldar, May 20 2022

Equals -1/4 + Sum_{k>=2} (-1)^k * k * (k - Sum_{i=2..k} zeta(i)) (Furdui, 2013). - Amiram Eldar, Jun 09 2022

Equals integral_1^oo {x}/x^3 dx where {.} is the fractional part. [Nahin]. R. J. Mathar, May 22 2024

Example

0.177532966575886781763792416676987405390525049396600781132220885314996264798...

Mathematica

RealDigits[1 - Pi^2/12, 10, 100][[1]] (* Amiram Eldar, May 20 2022 *)

Prog

(PARI) 1-Pi^2/12
(PARI) 1-zeta(2)/2

Crossrefs

Cf. A000290, A004125, A013661, A024916, A072691, A152416, A237593, A245092, A353908.

Sequence in context: A109939 A053011 A021133 * A336078 A074917 A154016

Adjacent sequences: A354235 A354236 A354237 * A354239 A354240 A354241

Keyword

nonn,cons,easy

Author

Omar E. Pol, May 20 2022

Status

approved