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Here is a pic showing An operator / function between addition and product.

It maps N x N to N.

It is commutative and associative.

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Tommy1729

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(0,n) -> 0

(1,n) -> n

Since that is trivial , it is not written in the picture.

So the table starts at 2.

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Tommy1729

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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).

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Tommy1729

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07/10/2016, 07:32 AM
(This post was last modified: 07/10/2016, 07:33 AM by Gottfried.)
The rowwise second order differences are not monotonously increasing. So what is this about?

Gottfried Helms, Kassel

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06/14/2022, 09:35 AM
(This post was last modified: 07/19/2022, 09:45 AM by Catullus.)
Tommy1729, Can you please tell us how it works.

It has been six years.

ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ

Please remember to stay hydrated.

Sincerely: Catullus

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(06/14/2022, 09:35 AM)Catullus Wrote: Six years later, and he has still not explained here how it works.

Perhaps interesting - an answer by me (2015) for

half-addition at MSE
Gottfried

Gottfried Helms, Kassel

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I had Many ideas that changed over time.

No proper solid definition or the sequence got stuck ( not definable or paradoxal ).

But one of the last versions of the idea was this ( doesnt match With the fitst picture But it was close. )

see pictures ;

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tommy1729

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I noticed staying to close to Sum gives issues.

Holding on to product longer works better.

There are still Many questions and fear of asympt to product or sum rather than in between…

Also one wonders If this approximates bennet base sqrt 2 or so.

See pictures.

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Tommy1729

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(06/25/2022, 09:27 PM)tommy1729 Wrote: I noticed staying to close to Sum gives issues.

Holding on to product longer works better.

There are still Many questions and fear of asympt to product or sum rather than in between…

Also one wonders If this approximates bennet base sqrt 2 or so.

See pictures.

Regards

Tommy1729

Notice the potential trend : f(x,x) = 5x - 6.

—-

Also one wonders how often values occur in the table.

If they never occur they are The analogue Numbers to primes.

And then one wonders About the growth of this sequence.

O ( 5 x / semilog(x) ) ??

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Tommy1729