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This is a cops-and-robbers if you are not familiar with the format click the tag to go to the wiki. There will not be a robbers' thread for this question.
Cops
Your task as Cops is to select two sequences from the Online Encyclopedia of Integer Sequences and write a program that takes the nth element of one sequence as input and outputs the nth element of the second sequence. You then make an answer including the code and omitting the sequences selected. Robbers will attempt to find the sequences you selected and if one manages to find the sequences you had in mind or some other sequences for which your program you must mark your answer as Cracked. If a robber informs you with a crack that you believe is not valid you may present a proof that it is not a crack. Otherwise you must mark it so.
As per the usual answers that have been uncracked for 7 days are eligible to be marked safe. A Cop may mark their answer as safe by revealing the sequences that they had in mind. Once safe an answer may no longer be cracked.
The goal is to minimize the byte count of your program while remaining uncracked.
Example
The following Python code translates the nth element of A000290 (the square numbers) into A000217 (the triangular numbers):
lambda x:sum(range(0,int(x**.5+1)))
Stipulations and Requirements
If you choose a sequence that has not been proven to be finite you must output all terms that might exist not just the ones listed on the OEIS page
As an exception to the previous rule languages without infinite precision integers do not have to output or input numbers outside of their range.
The size of your input sequence must not have been proven to be smaller than the output sequence.
Your input sequence must not have any repeat elements (otherwise the task is pretty much impossible)
The OEIS includes an index on their page (the first number after the "OFFSET" header) by default this is your offset for n (n equals the index for the first element on the sequence) if you choose another index you must indicate so in your answer.
If you choose a offset different from the one listed on the OEIS you must still map all elements in your input sequence to the corresponding element in your output sequence.
If your program receives an input that is not in the input sequence it may do whatever it wishes (undefined behavior). However it is probably in your best interest for it to still output an integer.
It is unsportsmanlike to intentionally make your code difficult to run, be it by making it time consuming to execute or through non-free language selection. While I will enforce the latter I cannot objectively enforce the former. However I implore you, for the sake of fun, not to attempt the former as it makes the challenge specifically more difficult for those with weaker computers.
Robbers
Your task as Robbers is to select uncracked, unsafe answers and find the sequences they map between. If you find solution a solution that works (not necessarily the Cops' intended solution) comment the sequences on the appropriate answer.
Robbers should not worry to much about verifying that two particular sequences are a solution, one should post a solution if it matches all of the entries on OEIS. If that is not the sequence that a cop had in mind the cop may offer a proof that it is incorrect or mark it as cracked if they cannot find one.
3How can a robber be sure that his answer is right for all inputs? Do they have to prove it mathematically? – Leo – 2017-02-15T18:41:35.857
"As per the usual answers that have been uncracked for 7 days can be marked safe." The "as per usual" should include that the answer is only safe once the intended solution has been revealed to ensure the answer's validity. – Martin Ender – 2017-02-15T18:44:44.590
1@Leo A robber should post a solution if it matches all of the entries on OEIS. If that is not the sequence that a cop had in mind they may offer a proof that it is incorrect or mark it as cracked if they cannot find one. I will update the robber's thread. – Post Rock Garf Hunter – 2017-02-15T18:50:26.640
Can a cop make a function that he cannot prove to be correct? For example, mapping Mersenne number to the corresponding even perfect number is correct iff there are no odd perfect numbers, which is unknown. The robber still can crack this, because he mustn't prove anything. But it looks like the first requirement bans such things, because the perfect number sequences has not proven to be finite and you can't also be sure that you output all the existing terms. – Wolfram – 2017-02-15T19:51:24.733
2It's hard to draw the line between common assumptions and unproven ideas. In the interest of clarity, I'd say you have to be able to prove that your answer works. – Dennis – 2017-02-15T20:25:25.230
@Wolfram I am going to have to side with Dennis at this point. You must be able to prove that your mapping will work. – Post Rock Garf Hunter – 2017-02-15T20:27:36.687
"If you choose a sequence that has not been proven to be finite you must output all terms that might exist not just the ones listed on the OEIS page", what about languages with no arbitrary big integers? – betseg – 2017-02-15T20:51:17.393
@betseg for finite languages you must only work up to the limit of you language. – Post Rock Garf Hunter – 2017-02-15T20:56:21.593
1
I have a feeling that some really nice solutions can be cracked in a dumb way like https://oeis.org/A000004 -> https://oeis.org/A000012
– Wolfram – 2017-02-16T00:40:23.267How come there is no robber's thread for this? – 0 ' – 2017-02-16T00:53:11.377
1@Wolfram Your input sequence must not have any repeat elements – Dennis – 2017-02-16T02:40:51.673
@1000000000 Because the robbers' thread's answers would consist of nothing but two OEIS identifiers. – Dennis – 2017-02-16T02:41:44.553
2@Dennis I guess that's a good point. It's a bummer though that there is no way for people to receive rep for finding cracks as it appears that that is pretty tricky for this challenge. – 0 ' – 2017-02-16T02:46:39.830