A355178 Decimal expansion of 2^(-2/3)/L, where L is the conjectured Landau's constant A081760.

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

Offset

1,3

Links

Table of n, a(n) for n=1..90.

Markus Faulhuber, An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a "Weltkonstante"-or-how Ramanujan split temperatures, The Ramanujan Journal volume 54, pages 1-27 (2021). See p. 23.

Formula

Equals A002580*A357318.

Equals A235362/A081760 = A235362*A175379/(A073005*A203145).

Equals Sum_{k,m in Z^2} exp(-Pi*(2/sqrt(3))*(k^2+k*m+m^2)).

From Gerry Martens, Jul 29 2023: (Start)

Equals hypergeom([1/3, 2/3], [1], 1/2).

Equals sqrt(Pi)/(Gamma(2/3)*Gamma(5/6)). (End)

Example

1.159595266963928365769992051570020881945...

Mathematica

First[RealDigits[N[2^(1/3)*Gamma[1/6]/(2Gamma[1/3]Gamma[5/6]), 90]]]

Crossrefs

Cf. A002580, A073005, A081760, A175379, A203145, A235362, A357318.

Sequence in context: A197693 A117014 A200283 * A010720 A094389 A057821

Adjacent sequences: A355175 A355176 A355177 * A355179 A355180 A355181

Keyword

nonn,cons

Author

Stefano Spezia, Sep 23 2022

Status

approved