[seqfan] Re: The two square composite sequence.

DAN_CYN_J dan_cyn_j at comcast.net
Mon Sep 2 04:08:00 CEST 2013


Hi Robert 
  
But they are 0(mod 3 or 5) composites and not allowed. 
  
Thanks for your input 

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

From: "Robert G. Wilson v" <rgwv at rgwv.com> 
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu> 
Sent: Sunday, September 1, 2013 8:12:10 PM 
Subject: [seqfan] Re: The two square composite sequence. 

  4,  81,  77 
  9, 100,  91 
 25, 144, 119 
 36, 169, 133 
  1, 144, 143 
 64, 225, 161 
  9, 196, 187 
121, 324, 203 

But also: 
  1,  16,  15 
  4,  25,  21 
  9,  64,  55 
 16,  25,   9 
 25,  64,  39 
 36, 121,  85 
 49,  64,  15 
 64, 121,  57 
 81, 196, 115 
100, 121,  21 
121, 324, 203 
144, 169,  25 
169, 256,  87 
196, 289,  93 
225, 484, 259 
256, 289,  33 
289, 324,  35 
324, 529, 205 
361, 400,  39 
400, 529, 129 
etc. 

Sincerely yours, Bob. 

-----Original Message----- 
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of DAN_CYN_J 
Sent: Sunday, September 01, 2013 5:10 PM 
To: Sequence Fanatics Discussion list 
Subject: [seqfan] The two square composite sequence. 



The two squares associated with each semi-prime composite. 

The rules for the simi-prime composite is no composite will be a 0(mod 3 or 
5) Each of it's two factors will be of equal length or 1 digit less like 
7*11 =77 is the first composite in the 3rd index of the sequence. The two 
previous index are just the two squares that is the solution to the 
composites two factors. 
So every third term is a composite and the two previous terms are it's 
associated squares as solutions. 
Which is the solution to x^2 - c = y^2 where c = a semi-prime composite and 
is known as the Fermat factoring method. 


The sequence begins -- 

4,81,77,9,100,91,25,144,119,36,169,133,1,144,143,64,225,161,9,196,187,121,32 
4,203... 

Dan 

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