- View SourceAn information type model of the primes applied to odd numbers:

Odd Numbers---------> Primes

^

I

Info function for Primes as Shannon Noise power function based on N=1/Log[n]

If the Info function is odd and the resulting odd number is prime,

you get a new set of primes that behave as "odd primes".

Using the code for this type of info model of the primes or composites

gives the sets:

digits=200

(* information function for the primes*)

f[n_]=If[PrimePi[n]-PrimePi[n-1]==1 ,n,0]

(* Primes*)

a=Table[f[n],{n,2,digits}]

{2,3,0,5,0,7,0,0,0,11,0,13,0,0,0,17,0,19,0,0,0,23,0,0,0,0,0,29,0,31,0,0,0,0,0,

37,0,0,0,41,0,43,0,0,0,47,0,0,0,0,0,53,0,0,0,0,0,59,0,61,0,0,0,0,0,67,0,0,0,

71,0,73,0,0,0,0,0,79,0,0,0,83,0,0,0,0,0,89,0,0,0,0,0,0,0,97,0,0,0,101,0,103,

0,0,0,107,0,109,0,0,0,113,0,0,0,0,0,0,0,0,0,0,0,0,0,127,0,0,0,131,0,0,0,0,0,

137,0,139,0,0,0,0,0,0,0,0,0,149,0,151,0,0,0,0,0,157,0,0,0,0,0,163,0,0,0,167,

0,0,0,0,0,173,0,0,0,0,0,179,0,181,0,0,0,0,0,0,0,0,0,191,0,193,0,0,0,197,0,

199,0}

(* information function for the Composites*)

g[n_]=If[1-(PrimePi[n]-PrimePi[n-1])==1 ,n,0]

(* composites*)

b=Table[g[n],{n,2,digits}]

{0,0,4,0,6,0,8,9,10,0,12,0,14,15,16,0,18,0,20,21,22,0,24,25,26,27,28,0,30,0,

32,33,34,35,36,0,38,39,40,0,42,0,44,45,46,0,48,49,50,51,52,0,54,55,56,57,58,

0,60,0,62,63,64,65,66,0,68,69,70,0,72,0,74,75,76,77,78,0,80,81,82,0,84,85,

86,87,88,0,90,91,92,93,94,95,96,0,98,99,100,0,102,0,104,105,106,0,108,0,110,

111,112,0,114,115,116,117,118,119,120,121,122,123,124,125,126,0,128,129,130,

0,132,133,134,135,136,0,138,0,140,141,142,143,144,145,146,147,148,0,150,0,

152,153,154,155,156,0,158,159,160,161,162,0,164,165,166,0,168,169,170,171,

172,0,174,175,176,177,178,0,180,0,182,183,184,185,186,187,188,189,190,0,192,

0,194,195,196,0,198,0,200}

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

Subject: SEQ FROM Roger L. Bagula

Date: Tue, 3 Feb 2004 13:11:57 -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All greater than and less than signs have been replaced by their html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 5,7,13,23,31,41,43,53,67,73,89,97,101,109,113,137,149,157,163,173,197,199,211,

223,227,239,241,251,263,277,281,293,307,317,331,337,347,349,359,379,389,419,

421,431,433,449,461,463,467,479,491,509,521,523,541,569,571,599,601,613,631,

641,643,647,659,661,673,677,691,719,733,739,751,769,797,811,827,829,859,863,

877,881,907,911,929,941,971,977,991,1009,1019,1021,1039,1051,1069,1087,1091,

1103,1117,1123,1151,1153,1171,1187,1201,1217,1231,1237,1249,1283,1289,1301,

1303,1319,1321,1367,1399,1423,1433,1439,1451,1453,1471,1483,1487,1489,1523,

1553,1571,1607,1609,1619,1621,1637,1657,1693,1709,1723,1741,1759,1777,1811,

1831,1847,1861,1867,1877,1879,1901,1913,1931,1933,1949,1951,1987,1999

%N A000001 Entropy power classification of primes as odd

%C A000001 Model based on entropy power for primes as odd numbers of:

N =1/log[n]

%F A000001 f[n_]=If[Mod[Floor[(2*n-1)/Log[2*n-1]],2]==1 ,2*n-1,0]

a(n)=If f[m] is prime then f[m]

%t A000001 digits=5*200

f[n_]=If[Mod[Floor[(2*n-1)/Log[2*n-1]],2]==1 ,2*n-1,0]

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@...), Feb 03 2004

RH

RA 209.179.200.221

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]