get a very good linear agreement with the primes

up to 1000, based on the entropy content of the primes.

I get an entropy constant very near:

3-E

The Prime based constant:

z0=Sum[PrimePi[n]/(n*Prime[n]),{n,1,Infinity}]

is very interesting as it increases the entropy as 1/n!

Since it is based on entropy development

this function should work even at very large

primes.

-------- Original Message --------

Subject: SEQ FROM Roger L. Bagula

Date: Wed, 3 Dec 2003 10:51:43 -0500 (EST)

From: <njas@...>

Reply-To: tftn@...

To: njas@...

CC: tftn@...

The following is a copy of the email message that was sent to njas

containing the sequence you submitted.

All greater than and less than signs have been replaced by their html

equivalents. They will be changed back when the message is processed.

This copy is just for your records. No reply is expected.

Subject: NEW SEQUENCE FROM Roger L. Bagula

%I A000001

%S A000001 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,

1531,1669,1723,1747,1801,1847,1871,1979,1987,2081,2089,2113,2129,2137,2207,

2239,2287,2311,2351,2383,2593,2609,2617,2699,2707,2731,2837,2861,3041,3049,

3181,3271,3313,3329,3469,3527,3593,3643,3659,3701,3709,3767,3851,3917,4001,

4027,4111,4273,4349,4409,4451,4639,4673,4723,4783,4817,4877,4903,4937,5039,

5081,5107,5167,5209,5261,5303,5381,5441,5449,5501,5527,5639,5657,5683,5717,

5743,5821,6029,6037,6133,6151,6203,6229,6247,6299,6317,6343,6361,6553,6571,

6737,6781,6869,6983,7027,7079,7159,7229,7247,7309,7433,7451,7477,7681,7699,

7717,7753,7841,7877,7993

%N A000001 A semi-empirical prime like function with primes isolated

%C A000001 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

%F A000001 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}]

%t A000001 (*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]

%O A000001 2

%K A000001 ,nonn,

%A A000001 Roger L. Bagula (tftn@...), Dec 03 2003

RH

RA 209.179.57.236

RU

RI

--

Respectfully, Roger L. Bagula

tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :

URL : http://home.earthlink.net/~tftn

URL : http://victorian.fortunecity.com/carmelita/435/

[Non-text portions of this message have been removed]