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 A094901 Positive integer values of the integer Schwarzian derivatives of the primes. 1
 0, 0, 3, 0, 3, 0, 0, 9, 0, 1, 1, 0, 0, 0, 8, 0, 1, 1, 0, 1, 0, 0, 3, 0, 0, 3, 0, 0, 14, 1, 9, 0, 32, 1, 0, 0, 0, 0, 8, 0, 32, 2, 3, 0, 0, 8, 1, 0, 0, 9, 0, 2, 0, 0, 8, 0, 1, 1, 0, 0, 12, 2, 0, 0, 5, 0, 30, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 29, 0, 32, 1, 1, 0, 0, 3, 0, 0, 0, 1, 1, 0, 3, 0, 0, 45, 0, 10, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 COMMENTS Negative values of the integer Schwarzian derivatives of Primes are much larger in magnitude than positives values. The significance of this seems to be in its relationship to zeta zeros on the complex plane. LINKS FORMULA a(n) = Floor[Abs[IntegerSchwarzianDerivative[Prime[n]]]] MATHEMATICA (* Ulam-Newton integer derivatives: *) f1[n_]=Prime[n]-Prime[n-1] f2[n_]=Prime[n]-2*Prime[n-1]+Prime[n-2] f3[n_]=Prime[n]-3*Prime[n-1]+3*Prime[n-2]-Prime[n-3] (* Integer Schwarzian derivative:*) sf[n_]=f3[n]/f1[n]-1.5*(f2[n]/f1[n])^2 af=Table[sf[n], {n, 4, 204}] a=Floor[Abs[af]] CROSSREFS Sequence in context: A165951 A300288 A340555 * A030220 A219240 A349612 Adjacent sequences: A094898 A094899 A094900 * A094902 A094903 A094904 KEYWORD nonn AUTHOR Roger L. Bagula, Jun 15 2004 STATUS approved

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Last modified December 4 09:27 EST 2022. Contains 358556 sequences. (Running on oeis4.)