A354051 Decimal expansion of Sum_{k>=0} 1 / (k^4 + 1).

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

Offset

1,2

Comments

Apart from leading digits the same as A256920. - R. J. Mathar, May 20 2022

Links

Table of n, a(n) for n=1..105.

Formula

Equals 1/2 + (Pi*(sinh(sqrt(2)*Pi) + sin(sqrt(2)*Pi))) / (2*sqrt(2)*(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi))).

Example

1.578477579667136838318022193245719235046672217327291327587486645793808...

Maple

evalf(1/2 + (Pi*(sinh(sqrt(2)*Pi) + sin(sqrt(2)*Pi))) / (2*sqrt(2)*(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi))), 105);

Mathematica

RealDigits[Chop[N[Sum[1/(k^4 + 1), {k, 0, Infinity}], 105]]][[1]]

Prog

(PARI) sumpos(k=0, 1/(k^4 + 1))

Crossrefs

Cf. A256920, A113319, A354052, A354053.

Cf. A002523, A255434, A354004.

Sequence in context: A070366 A339986 A141606 * A197491 A338595 A254274

Adjacent sequences: A354048 A354049 A354050 * A354052 A354053 A354054

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 16 2022, following a suggestion from Bernard Schott

Status

approved