With a functional Shannon entropy power of N=1/log(n)

this function misses the first three primes ,

but does very well in the lower primes after that.

Derivation goes like this from Shannon's formula

for the entropy power of white noise:

N1=(1/2*Pi*E)*Exp(2*H)

when ( linear transform of n to Prime[n] )

H=Log(Prime[n]/n)

then

N1=(E/(2*Pi))*Prime[n]/n

or

Prime[n]=2*Pi*n*N/E

and the asymptotic prime distribution function is:

PrimePi[n]--> n/Log(n)

which gives

N=1/Log(n)

as used here.

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

Subject: SEQ FROM Roger L. Bagula

Date: Sat, 31 Jan 2004 16:23:44 -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All greater than and less than signs have been replaced by their html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 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,

109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,

223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,

331

%N A000001 An entropy power of white noise function with N=1/log(n)

%C A000001 Function is based on asymptotic form of distribution:

PrimePi[n]--> n/log(n)

Function misses the first three primes {2,3,5} , but is pretty good after that.

%D A000001 Claude E. Shannon, The Mathematical Theory of Communications, page 63

%F A000001 a(n) = if Floor[2*Pi*n/(E*Log[n])] is prime then Floor[2*Pi*n/(E*Log[m])]

%t A000001 digits=5*200

f[n_]=Floor[2*Pi*n/(E*Log[n])]

a=Delete[Union[Table[If [PrimeQ[f[n]]==True,f[n],0],{n,2,digits}]],1]

%O A000001 2

%K A000001 ,nonn,

%A A000001 Roger L. Bagula (

tftn@...), Jan 31 2004

RH

RA 209.179.51.13

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/
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