First i for which the difference of the Riemann zeros r(i+1) - r(i) < 2^(-n) * I.
2, 9, 34, 186, 693, 1496, 4765, 44555, 95248, 420891, 1115578
-2
The first Riemann zero is at about 14.1347I. Data from Odlyzko was used to create this sequence. If the zeta function ever has a multiple zero, then this sequence would be constant after that point.
T. D. Noe, Plot of 11 terms
Andrew Odlyzko, Tables of zeros of the Riemann zeta function
Eric W. Weisstein, MathWorld: Riemann Zeta Function Zeros
(Mma) r = ReadSequenceFile["zero.txt"]; d = Differences[r]; Table[Position[d, _?(# < 2^(-n) &), 1, 1][[1, 1]], {n, -2, 8}]
Cf. S000540.
nonn,hard
T. D. Noe, Mar 19 2015