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A094901
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Positive integer values of the integer Schwarzian derivatives of the primes.
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0
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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; internal format)
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OFFSET
| 4,3
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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.
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FORMULA
| a(n) = Floor[Abs[IntegerSchwarzianDerivative[Prime[n]]]]
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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]]
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CROSSREFS
| Sequence in context: A126598 A127802 A165951 * A030220 A055240 A174559
Adjacent sequences: A094898 A094899 A094900 * A094902 A094903 A094904
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 15 2004
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