A094902 Average of four primes that have nonnegative integer Schwartzian derivative.

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.

Links

Table of n, a(n) for n=4..81.

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