A000035 is n mod 2, in case the site goes down or you're too lazy to check yourself. Charset:
023456789\`efu
Taking the "somehow still Turing-complete" route. I suppose I could've added 51 or so non-ASCII chars to improve my score, but that feels kind of like cheating.
Takes input through prompt and outputs through alert, and can be run in any modern browser.
Intended solution:
\u0046\u0075\u006e\u0063\u0074\u0069\u006f\u006e`\u0046\u0075\u006e\u0063\u0074\u0069\u006f\u006e\u0028\u0046\u0075\u006e\u0063\u0074\u0069\u006f\u006e\u0028\u0022\u0072\u0065\u0074\u0075\u0072\u006e\u0028\u0034\u0038\u0032\u002f\u0032\u0029\u002e\u0074\u006f\u0053\u0074\u0072\u0069\u006e\u0067\u0028\u0032\u0032\u0029\\u002\u0062\u0027\u0065\u0072\u0074\u0028\u0070\u0072\u006f\\u006\u0064\u0070\u0074\u0028\u0029\u0025\u0032\u0029\u0027\u0022\u0029\u0028\u0029\u0029\u0028\u0029```
which, when the escapes are removed, translates to
Function`Function(Function("return(482/2).toString(22)\u002b'ert(pro\u006dpt()%2)'")())()```
which simplifies again to
Function`Function(Function("return(482/2).toString(22)+'ert(prompt()%2)'")())()```
This works because JavaScript allows \uXXXX escapes in variable names (though not in arbitrary code, as Java does). The outer Function`code``` is necessary to run the code at all, since the entire thing needs to be escaped.
(If you're confused about how this works: JavaScript has something called tagged template literals, which for our purposes is just a function call on a string; it just uses f`string` instead of f("code"). So Function`code``` is about the same as Function("code")().)
Now, because of the lack of the hexadecimal chars 1abcd, we'll have to double-encode certain necessary characters such as the m in prompt(). So instead of \u006d, it becomes \\u006\u0064. But now we need to evaluate this as a string twice to make sure this gets fully decoded. (pro\u006dpt() would work just fine, but using \u002b as + would not.) This is what the second Function(code)() is for.
One further obstacle exists: there's no 1 in the charset, necessary to create an a from \u0061. So there's no way to generate an a by unescaping a string (I checked, the octal representation is \141). Instead, we can generate it with e.g. (20/2).toString(20). I went ahead and generated al in this manner because l would require double-escaping like m.
But the problem now is that the innermost Function call is now just generating a string. In order to actually execute it, we need to return it from the function and pass it to a third Function call. This we do, and finally our journey is complete.
*I am aware of using ${} within template literals, but those aren't in the charset, alright?
 
1Lower score is better? Or higher? So in essence we're trying to find a restricted character set that makes it difficult for someone else to make a program in the chosen language, after we've already worked out a solution? – BradC – 2017-07-27T16:56:15.893
1Do we need to use all the bytes in our set? I would guess yes but it should probably be specified in the challenge. – Shaggy – 2017-07-27T17:06:35.260
1@Shaggy generally no, you can includes others for red herrings, but robbers can use everything – Stephen – 2017-07-27T17:08:31.977
Do we count newlines as a separate byte or as \n? – JAD – 2017-07-27T17:13:41.760
@StepHen does that mean that you can include bytes that aren't even part of your language to get a higher score? – H.PWiz – 2017-07-27T17:16:36.993
@H.PWiz you'd have to ask WheatWizard about no-ops – Stephen – 2017-07-27T17:17:20.600
1Can robbers use the same byte twice or more? – Mr. Xcoder – 2017-07-27T17:19:08.043
1@mrxcoder I would think so, else we are just finding anagrams. – JAD – 2017-07-27T17:24:27.300
@Mr.Xcoder
You are then to secretly write a program in that language that computes the nth term sequence using only the bytes in the set.only the bytes in that set, so dupes are allowed – Stephen – 2017-07-27T17:50:59.423Do I understand right that the robber could (if characters allow) hardcode an enormous table of values corresponding to the b file? This could be hard for cops to avoid. – xnor – 2017-07-27T18:52:54.200
@xnor Yes that would be possible. The problem is OEIS sequence do not have rigorous specifications, so we can only confirm via test battery. – Post Rock Garf Hunter – 2017-07-27T19:51:34.387
1
What do you mean by "b-list"? Is that the list of terms shown on the page that has the "list", i.e. http://oeis.org/A000004/list ?
– Azulflame – 2017-07-27T23:21:20.4702
@Azulflame The b-files are files that are associated with each sequence the can be accessed by replacing the
– Post Rock Garf Hunter – 2017-07-27T23:47:00.373Awith aband appending a.txt. For example https://oeis.org/b4.txt would access the b-files for that sequence.Can the byteset contain non-printable-ASCII? (i.e. can I inflate my score by including 0x00-0x1f and 0x7f-0xff?) – Doorknob – 2017-07-28T03:40:44.823
@Doorknob Yes it can, the question is about chiefly about bytes and is agnostic to characters. – Post Rock Garf Hunter – 2017-07-28T03:50:42.830