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A094901 Positive integer values of the integer Schwarzian derivatives of the primes. 1

%I

%S 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,

%T 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,

%U 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

%N Positive integer values of the integer Schwarzian derivatives of the primes.

%C 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.

%F a(n) = Floor[Abs[IntegerSchwarzianDerivative[Prime[n]]]]

%t (* 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]]

%K nonn

%O 4,3

%A _Roger L. Bagula_, Jun 15 2004

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