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Implement a function \$f\$ (as a function or complete program), such that

\$ \displaystyle\lim_{n\rightarrow \infty} f(n) \$

converges to a number which is not a computable number.

Answers will be scored in bytes with fewer bytes being better.

IO formats

Your answer may be in any of the following formats

• A program or function that takes \$n\$ as input and outputs \$f(n)\$.
• A program or function that takes \$n\$ as input and outputs all \$f(m)\$ where \$m \leq n\$.
• A program or function that outputs successive members of the sequence indefinitely.

Numeric output can be given as any of the following

• An arbitrary precision rational type.
• A pair of arbitrary precision integers representing a numerator and denominator. e.g. \$(2334, 888)\$
• A string representing a rational expressed as a fraction. e.g. 2334/888
• A string representing a rational expressed as a decimal expansion. e.g. 3.141592

Use of fixed precision floating point numbers is unfortunately not accepted. They end up being messy when dealing with limits, I hope the options permitted allow the majority of languages to compete in this challenge relatively unencumbered.

Neither of the fractional outputs are required to be in reduced form.

Examples

Here are some numbers which are not computable, but are computable in the limit. That is any of the following numbers are potential limits for valid solutions to the challenge. This list is obviously not exhaustive.

• The real whose binary expansion encodes the halting problem.
• The real whose binary expansion encodes the busy beaver numbers.
• The real whose binary expansion encodes the truth set of first order logic.
• Chaitin's constant

posted

Implement a function \$f\$ (as a function or complete program), such that

\$ \displaystyle\lim_{n\rightarrow \infty} f(n) \$

converges to a number which is not a computable number.

Answers will be scored in bytes with fewer bytes being better.

IO formats

Your answer may be in any of the following formats

• A program or function that takes \$n\$ as input and outputs \$f(n)\$.
• A program or function that takes \$n\$ as input and outputs all \$f(m)\$ where \$m \leq n\$.
• A program or function that outputs successive members of the sequence indefinitely.

Numeric output can be given as any of the following

• An arbitrary precision rational type.
• A string representing a rational expressed as a fraction. e.g. 2334/888
• A string representing a rational expressed as a decimal expansion. e.g. 3.141592

Use of fixed precision floating point numbers is unfortunately not accepted. They end up being messy when dealing with limits, I hope the options permitted allow the majority of languages to compete in this challenge relatively unencumbered.

Examples

Here are some numbers which are not computable, but are computable in the limit. That is any of the following numbers are potential limits for valid solutions to the challenge. This list is obviously not exhaustive.

• The real whose binary expansion encodes the halting problem.
• The real whose binary expansion encodes the busy beaver numbers.
• The real whose binary expansion encodes the truth set of first order logic.
• Chaitin's constant

Implement a function \$f\$ (as a function or complete program), such that

\$ \displaystyle\lim_{n\rightarrow \infty} f(n) \$

converges to a number which is not a computable number.

Answers will be scored in bytes with fewer bytes being better.

IO formats

Your answer may be in any of the following formats

• A program or function that takes \$n\$ as input and outputs \$f(n)\$.
• A program or function that takes \$n\$ as input and outputs all \$f(m)\$ where \$m \leq n\$.
• A program or function that outputs successive members of the sequence indefinitely.

Numeric output can be given as any of the following

• An arbitrary precision rational type.
• A pair of arbitrary precision integers representing a numerator and denominator. e.g. \$(2334, 888)\$
• A string representing a rational expressed as a fraction. e.g. 2334/888
• A string representing a rational expressed as a decimal expansion. e.g. 3.141592

Use of fixed precision floating point numbers is unfortunately not accepted. They end up being messy when dealing with limits, I hope the options permitted allow the majority of languages to compete in this challenge relatively unencumbered.

Neither of the fractional outputs are required to be in reduced form.

Examples

Here are some numbers which are not computable, but are computable in the limit. That is any of the following numbers are potential limits for valid solutions to the challenge. This list is obviously not exhaustive.

• The real whose binary expansion encodes the halting problem.
• The real whose binary expansion encodes the busy beaver numbers.
• The real whose binary expansion encodes the truth set of first order logic.
• Chaitin's constant

Implement a function \$f\$ (as a function or complete program), such that

\$ \displaystyle\lim_{n\rightarrow \infty} f(n) \$

converges to a number which is not a computable number.

Answers will be scored in bytes with fewer bytes being better.

IO formats

Your answer may be in any of the following formats

• A program or function that takes \$n\$ as input and outputs \$f(n)\$.
• A program or function that takes \$n\$ as input and outputs all \$f(m)\$ where \$m \leq n\$.
• A program or function that outputs successive members of the sequence indefinitely.

Examples

Here are some numbers which are not computable, but are computable in the limit. That is any of the following numbers are potential limits for valid solutions to the challenge. This list is obviously not exhaustive.

• The real whose binary expansion encodes the halting problem.
• The real whose binary expansion encodes the busy beaver numbers.
• The real whose binary expansion encodes the truth set of first order logic.
• Chaitin's constant

Implement a function \$f\$ (as a function or complete program), such that

\$ \displaystyle\lim_{n\rightarrow \infty} f(n) \$

converges to a number which is not a computable number.

Answers will be scored in bytes with fewer bytes being better.

IO formats

Your answer may be in any of the following formats

• A program or function that takes \$n\$ as input and outputs \$f(n)\$.
• A program or function that takes \$n\$ as input and outputs all \$f(m)\$ where \$m \leq n\$.
• A program or function that outputs successive members of the sequence indefinitely.

Numeric output can be given as any of the following

• An arbitrary precision rational type.
• A string representing a rational expressed as a fraction. e.g. 2334/888
• A string representing a rational expressed as a decimal expansion. e.g. 3.141592

Use of fixed precision floating point numbers is unfortunately not accepted. They end up being messy when dealing with limits, I hope the options permitted allow the majority of languages to compete in this challenge relatively unencumbered.

Examples

Here are some numbers which are not computable, but are computable in the limit. That is any of the following numbers are potential limits for valid solutions to the challenge. This list is obviously not exhaustive.

• The real whose binary expansion encodes the halting problem.
• The real whose binary expansion encodes the busy beaver numbers.
• The real whose binary expansion encodes the truth set of first order logic.
• Chaitin's constant