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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
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.
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
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jun 15 2004
STATUS
approved