Is there an equation $f(k,m,n)=n$ where $n$ is the number of applications of the Ackermann function needed?

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Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$



Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?



Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.



Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.




recursion tetration hyperoperation ackermann-function




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  • Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
    – Mason
    Jul 15 at 4:40






  • 1




    @Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
    – user189728
    Jul 15 at 14:55










  • Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
    – Mason
    Jul 15 at 17:58










  • @Mason is there a simple way to migrate questions?
    – user189728
    Jul 15 at 17:59










  • Look it up on the Meta and post the link here. I dunno know. but I need to.
    – Mason
    Jul 15 at 17:59















up vote
0
down vote

favorite












Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$



Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?



Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.



Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.




recursion tetration hyperoperation ackermann-function




share|cite|improve this question





















  • Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
    – Mason
    Jul 15 at 4:40






  • 1




    @Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
    – user189728
    Jul 15 at 14:55










  • Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
    – Mason
    Jul 15 at 17:58










  • @Mason is there a simple way to migrate questions?
    – user189728
    Jul 15 at 17:59










  • Look it up on the Meta and post the link here. I dunno know. but I need to.
    – Mason
    Jul 15 at 17:59













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$



Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?



Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.



Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.




recursion tetration hyperoperation ackermann-function




share|cite|improve this question













Using the definition of the Ackermann function on page 247 of this paper, (sidenote, great paper):
$$
alpha(k,m,n) =
begincases
m+n, & k=1 \
m, & n=1 \
alpha(k-1,m,alpha(k,m,n-1)),& textotherwise
endcases
$$



Is there some function $f$ such that $f(k,m,n)$ returns the number of times $alpha$ is used to calculate $alpha(k,m,n)$?



Some trivial values would be $f(1,m,n)=f(k,m,1)=1$, and $f(2,2,2)=2$, found manually by counting the number of $alpha$s in the expanded form of $alpha$.



Note: There is neither a tag for "ackermann-function" or "recursion", I lack the privilege to create these but I feel they would have some limited use.





recursion tetration hyperoperation ackermann-function





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 10 at 12:50









Simply Beautiful Art

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asked Jul 15 at 4:05









user189728

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  • Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
    – Mason
    Jul 15 at 4:40






  • 1




    @Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
    – user189728
    Jul 15 at 14:55










  • Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
    – Mason
    Jul 15 at 17:58










  • @Mason is there a simple way to migrate questions?
    – user189728
    Jul 15 at 17:59










  • Look it up on the Meta and post the link here. I dunno know. but I need to.
    – Mason
    Jul 15 at 17:59

















  • Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
    – Mason
    Jul 15 at 4:40






  • 1




    @Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
    – user189728
    Jul 15 at 14:55










  • Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
    – Mason
    Jul 15 at 17:58










  • @Mason is there a simple way to migrate questions?
    – user189728
    Jul 15 at 17:59










  • Look it up on the Meta and post the link here. I dunno know. but I need to.
    – Mason
    Jul 15 at 17:59
















Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40




Your question doesn't make a whole lot of sense in the vocabulary of mathematics. Does there exist a function? Sure. You have just defined such a function. You mean is there a nice neat closed form? How many times does a recursive algorithm call upon itself might be a good CS question. I think your question might get more play on cs.stackexchange.com but I am not so sure of the community there and how they would respond.
– Mason
Jul 15 at 4:40




1




1




@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55




@Mason I initially intended to ask this on stackoverflow, but I felt it wasn't CS-related enough
– user189728
Jul 15 at 14:55












Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58




Oh no. Ackermann Function is right out of the CS Camp. They should be very interested: Check out: cs.stackexchange.com/questions/47227/…. The problem will be that you are going to have a more precise question to make much progress.
– Mason
Jul 15 at 17:58












@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59




@Mason is there a simple way to migrate questions?
– user189728
Jul 15 at 17:59












Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59





Look it up on the Meta and post the link here. I dunno know. but I need to.
– Mason
Jul 15 at 17:59
















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