[seqfan] Re: If 2 disappears

[Neil Sloane]

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 regards
Neil

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.com
Email: 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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