A391666 Decimal expansion of Sum_{k>=1} k * zeta(2*k) * Lucas(2*k) / 5^k.

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

Offset

1,1

Links

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

Kunle Adegoke, Problem H-955, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 63, No. 1 (2025), p. 124.

Formula

Equals (1/2) * c * tan(c) + 3 * (c / cos(c))^2, where c = Pi/(2*sqrt(5)) (A244979).

Example

2.838705933765362990635482356454462784619926485233502...

Mathematica

With[{c = Pi/(2*Sqrt[5])}, RealDigits[(1/2) * c * Tan[c] + 3 * (c / Cos[c])^2, 10, 120][[1]]]

Prog

(PARI) my(c = Pi/(2*sqrt(5))); (1/2) * c * tan(c) + 3 * (c / cos(c))^2

Crossrefs

Cf. A000032, A005248, A244979, A350760, A391665.

Sequence in context: A081349 A111445 A076696 * A011057 A082236 A337822

Adjacent sequences: A391663 A391664 A391665 * A391667 A391668 A391669

Keyword

nonn,cons

Author

Amiram Eldar, Dec 16 2025

Status

approved