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
Examples
0.59467812353527851916811426976055493760363946961024...
Links
- 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.
Programs
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Mathematica
RealDigits[(Pi/(2*Sqrt[5]))*Tan[Pi/(2*Sqrt[5])], 10, 100][[1]]
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).