|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|