OFFSET
1,1
COMMENTS
Conjecture 2: The zeta zeros whose indices are terms of this sequence are the locations where the zeta zero counting function, (RiemannSiegelTheta(t) + Im(log(zeta(1/2 + i*t))))/Pi + 1 overcounts the number of zeta zeros on the critical line.
Conjecture 3: This sequence consists of the numbers k such that sign(Im(zetazero(k)) - 2*Pi*e*exp(LambertW((k - 7/8)/e))) = 1. Verified for the first 100000 zeta zeros.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000
MATHEMATICA
(* Definition: *)
fQ[n_] := Block[{a = N[Im@ ZetaZero@ n, 32]}, Floor[a (Log[a] - Log[2Pi] - 1)/(2Pi) + 7/8] == n]; Select[ Range@ 1550, fQ] (* Robert G. Wilson v, Feb 21 2017 *)
(* Definition: *)
Monitor[Flatten[Position[Table[Floor[Im[ZetaZero[n]]/(2*Pi)*Log[Im[ZetaZero[n]]/(2*Pi*Exp[1])] + 7/8] - n + 1, {n, 1, 1500}], 1]], n]
(* Conjecture 3: *)
Monitor[Flatten[Position[Table[Sign[Im[ZetaZero[n]] - 2*Pi*E*Exp[LambertW[(n - 7/8)/E]]], {n, 1, 1500}], 1]], n]
CROSSREFS
KEYWORD
nonn
AUTHOR
Mats Granvik, Feb 21 2017
STATUS
approved