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February 23rd, 2010, 11:16 AM  #11  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: New sequence containing all the primes + some semiprime Quote:
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February 23rd, 2010, 11:19 AM  #12  
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Re: New sequence containing all the primes + some semiprime Quote:
22 and so on 14, 22,38 etc.... are on the sequence.  
February 23rd, 2010, 11:25 AM  #13  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: New sequence containing all the primes + some semiprime Quote:
 
February 23rd, 2010, 11:30 AM  #14  
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Re: New sequence containing all the primes + some semiprime Quote:
The sequence contains: All primes except those divisible by {2, 3} All semiprimes except those divisible by {2, 3} All 3almost primes except those divisible by {2, 3} ... All kalmost primes except those divisible by {2, 3} So 14,22,38 are divisible by 2 14,22,38 are semiprime I do not understand ....  
February 23rd, 2010, 12:20 PM  #15  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: New sequence containing all the primes + some semiprime Quote:
Quote:
"All primes are natural numbers" does not imply "No composites are natural numbers". "All numbers not divisible by 2 or 3 are in the sequence" does not imply "No numbers divisible by 2 or 3 are in the sequence".  
February 23rd, 2010, 04:00 PM  #16 
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Re: New sequence containing all the primes + some semiprime
I'm really dumb!

February 24th, 2010, 05:11 AM  #17  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: New sequence containing all the primes + some semiprime Quote:
for n odd and for n even. Maybe you can even prove which semiprimes divisible by 3 are in the sequence. I haven't done that.  

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