A391665 Decimal expansion of Sum_{k>=1} k * zeta(2*k) * Fibonacci(2*k) / 5^k.

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

Offset

1,3

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

Example

1.14446135243354716993453220873833924074118865161458...

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A001906, A244979, A350760, A391666.

Sequence in context: A006075 A342576 A370389 * A241295 A074904 A010304

Adjacent sequences: A391662 A391663 A391664 * A391666 A391667 A391668

Keyword

nonn,cons

Author

Amiram Eldar, Dec 16 2025

Status

approved