Minimum number of terms to uniquely identify a sequence

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As a rule of thumb, when searching the OEIS, you should enter six terms in the search box in order to obtain a manageably small plurality of results. Too many results makes the desired sequence a needle in the haystack, and too few (or none) might be of no help at all.

However, some sequences in the OEIS can be uniquely identified with fewer than six terms in the search box, and some require many more.

As the OEIS continues to expand, the information here may become outdated, perhaps causing some sequences to need more terms to uniquely identify than what is stated here.

One term is enough to uniquely identify

Of course, many sequences contain all integers, but because of term visibility only finitely many are searchable. Generally for a sequence to be identified by a single number it must be fairly large. For example, sequence A328078 is uniquely identified by term 820441299 (as of 2020). The smallest number uniquely identifying a sequence (also as of 2020) is 14919, in A212896. (You can get different results by looking only at signed terms.)

Two terms are enough to uniquely identify

If consecutive terms of a sequence are separated by distances other than 1, 2 or –1, the possibility exists that the sequence could be uniquely identified with just two terms. So, "703, 2110" uniquely identifies A161021.

Three terms are enough to uniquely identify

It seems that a lot of sequences in the OEIS are in ascending order. If a sequence is in neither ascending nor descending order, it might be possible to uniquely identify it by choosing a subsequence of three terms that proves the sequence is in neither ascending nor descending order. The search string "51, 154" could (and does) give sequences that are in ascending order, but "51, 154, 77" does not, instead narrowing down precisely to A008883, the Collatz sequence starting at 51. However, this particular example took some searching. A lot of Collatz sequences can be identified with just two terms, and most of the ones that can't be so isolated require more than twelve terms.

Twelve or more terms are needed to uniquely identify

Some sequences in the OEIS are contained in other sequences also in the OEIS, and so a lot of terms may be necessary to uniquely identify, and when that happens, it may be a consequence of term visibility more than anything else. For example, to make A008873 be the only result, you need at least twenty-one terms in the search box. Any fewer than that and A128333 will also come up as a result. That's because in the main entry page, display of the latter sequence is capped at the 62nd term, 161, which is the twentieth term of the former.

What about the prime numbers? You can try putting in all the terms showing for A000040, and you will still get at least four results besides that one.