|
|
A089070
|
|
A semi-empirical prime like function with primes isolated.
|
|
0
|
|
|
3, 5, 11, 79, 109, 131, 211, 223, 229, 241, 271, 277, 347, 353, 379, 443, 463, 509, 523, 557, 571, 577, 631, 727, 827, 877, 971, 1051, 1103, 1229, 1237, 1259, 1303, 1409, 1439, 1447, 1493, 1531, 1669, 1723, 1747, 1801, 1847, 1871, 1979, 1987, 2081, 2089
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
LINKS
|
|
|
MATHEMATICA
|
(*first entropy constant to n=10000*)
p0[n_]=PrimePi[n]/n
a=Table[ -p0[n]*Log[p0[n]], {n, 2, 10000}];
w0=N[Apply[Plus, a], 200]/10000
(*Second entropy constant to n=10000*)
z0=Sum[PrimePi[n]/(n*Prime[n]), {n, 1, 10000}];
(* semi-empirical prime-like function based on prime entropy sums*)
p[n_]=Sum[ -Log[PrimePi[i]/i], {i, 2, n}]
a0=Table[If[PrimeQ[Floor[p[n]*(2+E+z0/n+w0)]]==True, Floor[p[n]*(2+E+z0/n+w0)], 0], {n, 2, 1000}];
c0=Delete[Union[a0], 1]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,uned,obsc,less
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|