Pairs of integers ordered by their exponentiation code-golf sequence number

Output the infinite list of pairs of integers (a, b), where both \$ a > 1 \$ and \$ b > 1 \$, ordered by the value of \$ a^b \$. When there are multiple pairs where \$ a^b \$ is equal, they should be ordered lexicographically.

For example, \$ 2^4 = 4^2 = 16 \$, but (2, 4) should come before (4, 2), because it is lexicographically earlier.

This sequence starts:

2, 2 2, 3 3, 2 2, 4 4, 2 5, 2 3, 3 2, 5 6, 2 7, 2 

Here are the first 100,000 pairs: https://gist.github.com/pxeger/0974c59c38ce78a632701535181ccab4

Rules

• As with standard sequence challenges, you may choose to either:
  • Take an input \$ n \$ and output the \$ n \$th pair in the sequence
  • Take an input \$ n \$ and output the first \$ n \$ pairs
  • Output the sequence indefinitely, e.g. using a generator
• You may use \$ 0 \$- or \$ 1 \$-indexing
• You may use any standard I/O method
• Standard loopholes are forbidden
• This is code-golf, so the shortest code in bytes wins

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Pairs of integers ordered by their exponentiation

Pairs of integers ordered by their exponentiation code-golf sequence number

Output the infinite list of pairs of integers (a, b), where both \$ a > 1 \$ and \$ b > 1 \$, ordered by the value of \$ a^b \$. When there are multiple pairs where \$ a^b \$ is equal, they should be ordered lexicographically.

For example, \$ 2^4 = 4^2 = 16 \$, but (2, 4) should come before (4, 2), because it is lexicographically earlier.

This sequence starts:

2, 2 2, 3 3, 2 2, 4 4, 2 5, 2 3, 3 2, 5 6, 2 7, 2 

Here are the first 200 pairs: https://gist.github.com/pxeger/30378e618415ea9cea7961e0f0381e75

Rules

• As with standard sequence challenges, you may choose to either:
  • Take an input \$ n \$ and output the \$ n \$th pair in the sequence
  • Take an input \$ n \$ and output the first \$ n \$ pairs
  • Output the sequence indefinitely, e.g. using a generator
• You may use \$ 0 \$- or \$ 1 \$-indexing
• You may use any standard I/O method
• Standard loopholes are forbidden
• This is code-golf, so the shortest code in bytes wins

Meta

• Is this clear enough?
• Is this a duplicate?

Pairs of integers ordered by their exponentiation code-golf sequence number

Output the infinite list of pairs of integers (a, b), where both \$ a > 1 \$ and \$ b > 1 \$, ordered by the value of \$ a^b \$. When there are multiple pairs where \$ a^b \$ is equal, they should be ordered lexicographically.

For example, \$ 2^4 = 4^2 = 16 \$, but (2, 4) should come before (4, 2), because it is lexicographically earlier.

This sequence starts:

2, 2 2, 3 3, 2 2, 4 4, 2 5, 2 3, 3 2, 5 6, 2 7, 2 

Here are the first 100,000 pairs: https://gist.github.com/pxeger/0974c59c38ce78a632701535181ccab4

Rules

• As with standard sequence challenges, you may choose to either:
  • Take an input \$ n \$ and output the \$ n \$th pair in the sequence
  • Take an input \$ n \$ and output the first \$ n \$ pairs
  • Output the sequence indefinitely, e.g. using a generator
• You may use \$ 0 \$- or \$ 1 \$-indexing
• You may use any standard I/O method
• Standard loopholes are forbidden
• This is code-golf, so the shortest code in bytes wins

Meta

• Is this clear enough?
• Is this a duplicate?

Pairs of integers ordered by their exponentiation code-golf sequence number

Output the infinite list of pairs of integers (a, b), where both \$ a > 1 \$ and \$ b > 1 \$, ordered by the value of \$ a^b \$. When there are multiple pairs where \$ a^b \$ is equal, they should be ordered lexicographically.

For example, \$ 2^4 = 4^2 = 16 \$, but (2, 4) should come before (4, 2), because it is lexicographically earlier.

This sequence starts:

2, 2 2, 3 3, 2 2, 4 4, 2 5, 2 3, 3 2, 5 6, 2 7, 2 

Here are the first 200 pairs: https://gist.github.com/pxeger/989319603a0e526e2849d05bcd40e3eb

Rules

• As with standard sequence challenges, you may choose to either:
  • Take an input \$ n \$ and output the \$ n \$th pair in the sequence
  • Take an input \$ n \$ and output the first \$ n \$ pairs
  • Output the sequence indefinitely, e.g. using a generator
• You may use \$ 0 \$- or \$ 1 \$-indexing
• You may use any standard I/O method
• Standard loopholes are forbidden
• This is code-golf, so the shortest code in bytes wins

Meta

• Is this clear enough?
• Is this a duplicate?

Pairs of integers ordered by their exponentiation code-golf sequence number

Output the infinite list of pairs of integers (a, b), where both \$ a > 1 \$ and \$ b > 1 \$, ordered by the value of \$ a^b \$. When there are multiple pairs where \$ a^b \$ is equal, they should be ordered lexicographically.

For example, \$ 2^4 = 4^2 = 16 \$, but (2, 4) should come before (4, 2), because it is lexicographically earlier.

This sequence starts:

2, 2 2, 3 3, 2 2, 4 4, 2 5, 2 3, 3 2, 5 6, 2 7, 2 

Here are the first 200 pairs: https://gist.github.com/pxeger/30378e618415ea9cea7961e0f0381e75

Rules

• As with standard sequence challenges, you may choose to either:
  • Take an input \$ n \$ and output the \$ n \$th pair in the sequence
  • Take an input \$ n \$ and output the first \$ n \$ pairs
  • Output the sequence indefinitely, e.g. using a generator
• You may use \$ 0 \$- or \$ 1 \$-indexing
• You may use any standard I/O method
• Standard loopholes are forbidden
• This is code-golf, so the shortest code in bytes wins

Meta

• Is this clear enough?
• Is this a duplicate?