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Between addition and product ( pic )
#1
Here is a pic showing An operator / function between addition and product.

It maps N x N to N.

It is commutative and associative.

Regards

Tommy1729


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#2
(0,n) -> 0
(1,n) -> n

Since that is trivial , it is not written in the picture.
So the table starts at 2.

Regards

Tommy1729
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#3
Its nice that they are all Natural numbers too

How are they being calculated?

the first 3 lines can be found in oeis databank



https://oeis.org/search?q=4%2C5%2C7%2C9%...&go=Search

https://oeis.org/search?q=5%2C8%2C9%2C13...&go=Search

https://oeis.org/search?q=7%2C9%2C12%2C1...&go=Search
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#4
My apologies for the delay.

I have been thinking about this rather than writing.

I would like to know more before i say more.

Its all very new.

But i can say this is about hyperoperators and a half iterate of 2^(z+1).

Regards

Tommy1729
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#5
The rowwise second order differences are not monotonously increasing. So what is this about?
Gottfried Helms, Kassel
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