A350760 Decimal expansion of Pi/(2*sqrt(5)) * tan(Pi/(2*sqrt(5))).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Robert Frontczak, Problem B-1267, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 58, No. 2 (2020), p. 179; The Zeta Riemann Function and the Cotangent Function, Solution to Problem B-1267 by Brian Bradie, ibid., Vol. 59, No. 2 (2021), pp. 179-180.

Formula

Equals Sum_{n>=1} zeta(2*n)*Fibonacci(2*n)/5^n (Frontczak, 2020).

Equals -1 + Sum_{n>=1} zeta(2*n)*Lucas(2*n)/5^n (Frontczak, 2020).

Equals Sum_{n>=0} 1/A273366(n).

Example

0.59467812353527851916811426976055493760363946961024...

Mathematica

RealDigits[(Pi/(2*Sqrt[5]))*Tan[Pi/(2*Sqrt[5])], 10, 100][[1]]

Crossrefs

Cf. A000032, A000045, A062786, A244979.

Sequence in context: A342204 A010774 A272610 * A340216 A198748 A196754

Adjacent sequences: A350757 A350758 A350759 * A350761 A350762 A350763

Keyword

nonn,cons

Author

Amiram Eldar, Jan 14 2022

Status

approved