A378131 Decimal expansion of sqrt(1 + sqrt(3))*L/(Pi*12^(1/8)), where L is the lemniscate constant (A062539).

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

Offset

1,5

Links

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

Wikipedia, Lemniscate constant (includes this constant).

Index to sequences related to the Gamma function.

Formula

Equals sqrt((1 + sqrt(3))*Pi)/(2^(3/4)*3^(1/8)*Gamma(3/4)^2) = sqrt(A090388*A000796)/(2^(3/4)*3^(1/8)*A068465^2).

Equals Sum_{j,k integers} exp(-2*Pi*(j^2 + j*k + k^2)).

Equals 2F1(1/3, 2/3, 1, (3*sqrt(3) - 5)/4), where 2F1 is the ordinary hypergeometric function.

Example

1.011204695537690090572855988569625803283536658...

Mathematica

First[RealDigits[Sqrt[(1 + Sqrt[3])*Pi]/(2^(3/4)*3^(1/8)*Gamma[3/4]^2), 10, 100]] (* or *)
First[RealDigits[Hypergeometric2F1[1/3, 2/3, 1, (3*Sqrt[3] - 5)/4], 10, 100]]

Crossrefs

Cf. A000796, A062539, A068465, A090388.

Cf. A377999, A378128, A378129, A378130, A378132.

Sequence in context: A066659 A343468 A287846 * A085623 A317965 A369025

Adjacent sequences: A378128 A378129 A378130 * A378132 A378133 A378134

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 18 2024

Status

approved