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 A106636 Pair rational approximations of Zeta zeros as an integer sequence. 0
 9, 13, 16, 19, 21, 24, 26, 28, 31, 32, 34, 36, 38, 39, 41, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 56, 59, 60, 61, 63 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The average error in the approximation is low (-0.0559729 )for the first 30 zeta zeros. The idea is that the imaginary part of the zeta zero is a bad rational approximation of the type: 4/(a(n)+4) to give b[n]=2*Pi*(a(n)+4)/4 Pair rational is ( this sequence) : a(n)/(a(n)+4) LINKS FORMULA ZetaZero[n]=1/2+I*b[n] a(n) = Round[2*b[n]/Pi] MATHEMATICA (* Zeta Zero data from FindRoot *) z = 0.5+ 14.1347251293669318` I; z = 0.5+ 21.0220394302515201` I; z = 0.5+ 25.0108575810860855` I; z = 0.5+ 30.4248761260581268` I; z = 0.5+ 32.935061587739185`I; z = 0.5 + 37.5861781581133191` I; z = 0.5+ 40.9187190119943267` I; z = 0.5+ 43.327073280866557` I; z = 0.5+ 48.0051508794884007` I; z = 0.5 + 49.7738324775595852` I; z = 0.5+ 52.97032147771447` I; z = 0.5+ 56.44624769706339` I; z = 0.5+ 59.34704400260235` I; z = 0.5 + 60.8317785246098` I; z = 0.5+ 65.1125440480816` I; z = 0.5+ 65.1125440480816` I; z = 0.5+ 67.07981052949417` I; z = 0.5 69.54640171117398` I; z = 0.5+ 72.0671576744819` I; z = 0.5+ 75.70469069908393` I; z = 0.5 + 77.14484006887483` I; z = 0.5+ 79.33737502024937` I; z = 0.5 + 82.91038085408603` I; z = 0.5+ 84.73549298051705` I; z = 0.5+ 87.42527461312524` I; z = 0.5+ 87.42527461312524` I; z = 0.5 + 92.49189927055848` I; z = 0.5 + 94.65134404051992` I; z = 0.5 + 95.87063422824534` I; z = 0.5+ 98.8311942181937` I; a = Table[Round[2*Im[z[n]]/Pi ], {n, 0, 29}] averageError=Apply[Plus, Table[2*Im[z[n]]/Pi - Round[2*Im[z[n]]/Pi ], {n, 0, 29}]]/30 CROSSREFS Sequence in context: A065977 A294999 A153051 * A186427 A050109 A294357 Adjacent sequences:  A106633 A106634 A106635 * A106637 A106638 A106639 KEYWORD nonn,uned AUTHOR Roger L. Bagula, May 11 2005 STATUS approved

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Last modified August 14 13:51 EDT 2020. Contains 336481 sequences. (Running on oeis4.)