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MatsGranvik

Sequence A282896 in the OEIS

Jun 21st, 2017
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  1. (* Sequence A282896 in the OEIS *)
  2. (*Comment 1:*)Monitor[
  3. Flatten[Position[
  4. Table[Floor[
  5. Im[ZetaZero[n]]/(2*Pi)*Log[Im[ZetaZero[n]]/(2*Pi*E)] + 11/8] -
  6. n + 1, {n, 1, 110}], 1]], n]
  7. (*Comment 2:*)
  8. Monitor[Flatten[
  9. Position[Table[
  10. Sign[Im[Zeta[1/2 + I*2*Pi*E*Exp[LambertW[(n - 11/8)/E]]]]], {n, 1,
  11. 110}], -1]], n]
  12. (*From Mats Granvik,Jun 17 2017:(Start)*)
  13. (*Comment 3:*)Flatten[
  14. Position[Table[
  15. Floor[2*(RiemannSiegelTheta[Im[ZetaZero[n]]]/Pi -
  16. Floor[RiemannSiegelTheta[Im[ZetaZero[n]]]/Pi])], {n, 1, 110}],
  17. 1]]
  18. (*Comment 3:*)
  19. Flatten[Position[
  20. Floor[2*FractionalPart[
  21. N[RiemannSiegelTheta[Im[ZetaZero[Range[110]]]]/Pi, 30]]], 1]]
  22. (*Comment 4:*)
  23. Clear[nn, n, k, t, FrancaLeclair, NumberOfZetaZeros];
  24. nn = 110;
  25. FrancaLeclair[n_] = 2*Pi*Exp[1]*Exp[ProductLog[(n - 11/8)/Exp[1]]];
  26. NumberOfZetaZeros[t_] =
  27. RiemannSiegelTheta[t]/Pi + Im[Log[Zeta[1/2 + I*t]] + I*Pi]/Pi;
  28. Monitor[b =
  29. N[Table[-(1 +
  30. 2*Sum[(NumberOfZetaZeros[FrancaLeclair[k + 1]] -
  31. 1) - (NumberOfZetaZeros[FrancaLeclair[k]] - 1) - 1, {k,
  32. 1, n}]), {n, 0, nn - 1}]], n];
  33. (*Notice that sequence b is integer in itself despite the use of the \
  34. Round function below:*)
  35. Flatten[Position[Round[b], 1]]
  36. (*End*)
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