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A282794 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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture 1: The union of a(n) and A282793 is A153815.

Conjecture 2: The zeta zeros with indices = a(n), are the locations where the zeta zero counting function: (RiemannSiegelTheta(t) + Im(log(zeta(1/2 + I*t))))/Pi + 1, undercounts 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 - 15/8)/e))) = -1. Verified for the 100000 first zeta zeros.

LINKS

Table of n, a(n) for n=1..35.

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]

(* Conjecture 3: *)

Monitor[Flatten[Position[Table[Sign[Im[ZetaZero[n]] - 2*Pi*E*Exp[LambertW[(n - 15/8)/E]]], {n, 1, 1500}], -1]], n]

CROSSREFS

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

Sequence in context: A165337 A256925 A235285 * A304606 A264951 A264958

Adjacent sequences:  A282791 A282792 A282793 * A282795 A282796 A282797

KEYWORD

nonn

AUTHOR

Mats Granvik, Feb 21 2017

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)