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There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting functionEquivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

(I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but a single and arbitrarily large one. It should be clear that I am not interested in those but in pairs that are not adjusted to each other this way.)

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

(I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but a single and arbitrarily large one. It should be clear that I am not interested in those but in pairs that are not adjusted to each other this way.)

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

(I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but a single and arbitrarily large one. It should be clear that I am not interested in those but in pairs that are not adjusted to each other this way.)

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Hans-Peter Stricker
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There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

Edit: To make things clear: I(I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but onea single and aribitrarilyarbitrarily large one. It should be clear that I am not interested in those but in pairs that are not adjusted to each other this way.)

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

Edit: To make things clear: I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but one single and aribitrarily large one. It should be clear that I am not interested in those.

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

(I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but a single and arbitrarily large one. It should be clear that I am not interested in those but in pairs that are not adjusted to each other this way.)

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Hans-Peter Stricker
  • 9.7k
  • 5
  • 53
  • 113

Longest coinciding pair of integer sequences known

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by default, but I may be mistaken about that.

One is disadviced to draw any conclusions from coincidences of integer sequences unless its proven, that they coincide for all $n$. (Even then there may be no sensible conclusions, as I have learned here: Equivalence of families of objects with the same counting function.)

In any case, it is hard not to be entrapped to draw a conclusion when $N$ is very large. But what is "very large"? Thus my question:

What is the largest $N$ with two known integer sequences coinciding upto $N$ but differing for an $n > N$?

(Can this information be captured from OEIS by an intelligent query?)

Edit: To make things clear: I am aware of the fact that one can trivially define pairs of integer sequences which conincide for all $n$ but one single and aribitrarily large one. It should be clear that I am not interested in those.