According to the Riemann Hypothesis, all zeroes of the Riemann zeta function are either negative even integers (called trivial zeroes) or complex numbers of the form
1/2 ± i*t for some real
t value (called non-trivial zeroes). For this challenge, we will be considering only the non-trivial zeroes whose imaginary part is positive, and we will be assuming the Riemann Hypothesis is true. These non-trivial zeroes can be ordered by the magnitude of their imaginary parts. The first few are approximately
0.5 + 14.1347251i, 0.5 + 21.0220396i, 0.5 + 25.0108576i, 0.5 + 30.4248761i, 0.5 + 32.9350616i.
Given an integer
N, output the imaginary part of the
Nth non-trivial zero of the Riemann zeta function, rounded to the nearest integer (rounded half-up, so
13.5 would round to
- The input and output will be within the representable range of integers for your language.
- As previously stated, for the purposes of this challenge, the Riemann Hypothesis is assumed to be true.
- You may choose whether the input is zero-indexed or one-indexed.
The following test cases are one-indexed.
1 14 2 21 3 25 4 30 5 33 6 38 7 41 8 43 9 48 10 50 50 143 100 237
This is OEIS sequence A002410.