[seqfan] Re: If 2 disappears

[Ali Sada]

Thank you Dr. Sloane for your response. I really appreciate it.

I just learned that Robert Dougherty-Bliss already wrote a paper called:

“The Number 2 Does Not Exist, And other p-removed primes”.  

I think it would be better if he adds the sequence to the OEIS since he obviously thought more thoroughly about the idea (and I ran out of my 3-sequence quota).

On a similar note, when I thought about "If 1 was the first prime" I found out that there is already a sequence in the OEIS in this regard. It is Anti Karttunen's A064989. 

It is fascinating to see that people, from different backgrounds, independently come up with the same ideas. This is another great thing about the OEIS; it allows us to see how similar we are!  

Best Regards,

Ali 



    On Thursday, December 19, 2019, 1:48:24 PM EST, Neil Sloane <njasloane at gmail.com> wrote:  
 
 To start with, I edited A232803 to give it a more explicit description.
Now Ali's "natural numbers" sequence, 1, 3, 4, 9, 5, 12, 6, 27, 16, 15, 7, 36, 8, 18, 20, 81, 10, 48, 11, 45, 24, 21, 13, 108, 25, 24, 64, 54, 14, 60, 17, 243, 28, . . . [I did not check it] can be described as "Products of terms of A232803", with a comment about how these would arise as "natural numbers"  if 2 were not a prime.
And, yes, certainly submit it to the OEIS!

Best regardsNeil 
Neil J. A. Sloane, President, OEIS Foundation.11 South Adelaide Avenue, Highland Park, NJ 08904, USA.Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.Phone: 732 828 6098; home page: http://NeilSloane.comEmail: njasloane at gmail.com


On Thu, Dec 19, 2019 at 12:25 PM Ali Sada via SeqFan <seqfan at list.seqfan.eu> wrote:


Hi Everyone, 

Because of a programming mistake, 2 disappeared. Subsequently, the prime numbers sequence changed. 
4,8, and 2p became “primes.” 
The new “prime numbers” sequence is:
3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 79, 82, 83, 86, 89, 94, 97, . . .  (A232803)

Now, the program tries to reconstruct the natural numbers using their prime factors:
a(1) = 1
a(2) = p1
a(3) = p2
a(4) = p1*p1
a(5) = p3
a(6) = p1*p2
etc.

Because of the mistake, the “natural numbers” sequence became:
1, 3, 4, 9, 5, 12, 6, 27, 16, 15, 7, 36, 8, 18, 20, 81, 10, 48, 11, 45, 24, 21, 13, 108, 25, 24, 64, 54, 14, 60, 17, 243, 28, . . .
(Obviously, 2 disappeared as a number, not as a digit.)
Because we have more primes, there will be more natural numbers, i.e. some numbers will appear more than once. What are these number? 

I would really appreciate it if you tell me this is a suitable sequence for the OEIS. 

Best,

Ali
 




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