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A282793 Indices n of nontrivial Riemann zeta zeros such that floor(Im(zetazero(n))/(2*Pi)*log(Im(zetazero(n))/(2*Pi*e)) + 7/8) - n + 1 = 1. 7
127, 196, 233, 289, 368, 380, 401, 462, 519, 568, 596, 619, 627, 655, 669, 693, 716, 729, 767, 796, 820, 849, 858, 888, 965, 996, 1029, 1035, 1044, 1114, 1179, 1210, 1251, 1277, 1291, 1308, 1332, 1343, 1431, 1457, 1488, 1496, 1499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture 1: The union of a(n) and A282794 is A153815.

Conjecture 2: The zeta zeros with indices = a(n) are the locations where the zeta zero counting function f(n) = (RiemannSiegelTheta(t) + Im(log(zeta(1/2 + I*t))))/Pi + 1 overcounts the number of zeta zeros on the critical line.

Conjecture 3: a(n) is the numbers n such that sign(Im(zetazero(n)) - 2*Pi*e*exp(LambertW((n - 7/8)/e)))=1. Verified for the 100000 first 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

Cf. A002505, A135297, A153815, A273061, A282793, A282794, A282896, A282897.

Sequence in context: A095284 A127579 A107380 * A180539 A195377 A142090

Adjacent sequences:  A282790 A282791 A282792 * A282794 A282795 A282796

KEYWORD

nonn

AUTHOR

Mats Granvik, Feb 21 2017

STATUS

approved

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Last modified February 18 03:33 EST 2020. Contains 332006 sequences. (Running on oeis4.)