A089070 A semi-empirical prime like function with primes isolated.

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

Offset

2,1

Links

Table of n, a(n) for n=2..49.

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

Sequence in context: A206640 A182354 A046928 * A232536 A168040 A068157

Adjacent sequences: A089067 A089068 A089069 * A089071 A089072 A089073

Keyword

nonn,uned,obsc,less

Author

Roger L. Bagula, Dec 03 2003

Status

approved