A282794 - OEIS

%I #41 Aug 31 2021 01:10:08

%S 136,213,256,379,399,509,531,580,639,696,705,779,795,809,871,994,1018,

%T 1048,1073,1088,1096,1113,1137,1158,1167,1209,1233,1265,1296,1321,

%U 1331,1346,1404,1445,1487

%N 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.

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

%C 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.

%C 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.

%t (* Definition: *)

%t 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]

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

%K nonn

%O 1,1

%A _Mats Granvik_, Feb 21 2017