A282794 Indices k of nontrivial Riemann zeta zeros such that floor(Im(zetazero(k))/(2*Pi)*log(Im(zetazero(k))/(2*Pi*e)) + 7/8) - k + 1 = -1.

136, 213, 256, 379, 399, 509, 531, 580, 639, 696, 705, 779, 795, 809, 871, 994, 1018, 1048, 1073, 1088, 1096, 1113, 1137, 1158, 1167, 1209, 1233, 1265, 1296, 1321, 1331, 1346, 1404, 1445, 1487

Offset: 1

Author

Mats Granvik, Feb 21 2017

Keywords

• nonn

Comments

Conjecture 1: The union of this sequence and A282793 is A153815.

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, undercounts the 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 - 15/8)/e))) = -1. Verified for the first 100000 zeta zeros.

Crossrefs

Cf. A002505, A135297, A153815, A273061, A282793, A282896, A282897.

Programs

Mathematica

(* 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]