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%I #5 Mar 30 2012 17:34:14
%S 0,13,0,24,0,36,0,0,60,0,0,84,0,0,0,120,0,0,145,0,162,0,0,0,204,0,216,
%T 0,0,254,0,278,0,298,0,0,330,0,0,362,0,381,0,0,0,0,445,456,0,0,482,0,
%U 506,520,0,540,0,0,567,0,0,612,624,0,0,666,0,693,0,0,0,739,0,762,0,0,798,0
%N Average of four primes that have nonnegative integer Schwartzian derivative.
%C Generally there seem to be more negative values than positive for the integer Schwarzian derivative of the Primes. The nearest primes to this average are the places where the prime curve has positive derivative, for example 13,23,37,61,83, etc.
%F a(n) = if Sf(Prime[n])>=0 then (Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/2 else zero
%t 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] sf[n_]=f3[n]/f1[n]-1.5*(f2[n]/f1[n])^2 a=Table[If[sf[n]>0\[Or]sf[n]==0, (Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/2, 0], {n, 4, 204}]
%K nonn
%O 4,2
%A _Roger L. Bagula_, Jun 15 2004
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