Numbers n such that the distance between Riemann zeros r(n+1) - r(n) is a new minimum.
1, 2, 4, 7, 9, 13, 19, 24, 27, 34, 63, 71, 91, 135, 159, 186, 212, 298, 315, 363, 453, 693, 922, 1496, 3777, 4765, 6709, 18859, 44555, 73997, 82552, 87761, 95248, 354769, 415587, 420891, 1115578
1
Note that the Mathematica program does not use approximate values of the zeta function. We treat the zeros that are on the critical line. Beyond the 10000th zero, we use Odlyzko’s table of the first 2001052 zeros.
T. D. Noe, Plot of 37 terms
Andrew Odlyzko, Tables of zeros of the Riemann zeta function
Eric W. Weisstein, MathWorld: Critical Line
Eric W. Weisstein, MathWorld: Riemann Zeta Function Zeros
(Mma) mx = Infinity; t = {}; i = 1; Do[s = Im[ZetaZero[i+1] - ZetaZero[i]]; If[s < mx, mx = s; AppendTo[t, i]], {i, 1000}]; t
Cf. A254297 (reports n+1).
nonn,hard,more,nice
T. D. Noe, Mar 17 2015