The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A282793 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. 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 this sequence and A282794 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 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 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)] + 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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)