login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

COMMENTS

The Wanged it function: p[n_]=Sum[ -Log[PrimePi[i]/i],{i,2,n}] Is a new type of Prime function that represents the build up of entropy in the Primes. Also the constant is approximately five( or w0~3-E): 2+E+w0~5

LINKS

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

FORMULA

p[n_]=Sum[ -Log[PrimePi[i]/i], {i, 2, n}] a=Table[If[PrimeQ[Floor[p[n]*(2+E+z0/n+w0)]]==True, Floor[p[n]*(2+E+z0/n+w0)], 0], {n, 2, 1000}]

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

AUTHOR

Roger L. Bagula, Dec 03 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 09:46 EDT 2022. Contains 356977 sequences. (Running on oeis4.)