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 A094902 Average of four primes that have nonnegative integer Schwartzian derivative. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS 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. LINKS FORMULA a(n) = if Sf(Prime[n])>=0 then (Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/2 else zero MATHEMATICA 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}] CROSSREFS Sequence in context: A114782 A065112 A114783 * A252056 A096069 A180265 Adjacent sequences:  A094899 A094900 A094901 * A094903 A094904 A094905 KEYWORD nonn AUTHOR Roger L. Bagula, Jun 15 2004 STATUS approved

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Last modified June 27 19:31 EDT 2022. Contains 354898 sequences. (Running on oeis4.)