Term visibility

Term visibility refers to the range of integers visible for a given sequence in the OEIS. In the theoretical sense, each sequence in the OEIS contains all numbers addressed by its definition or description, but in the practical sense, only a subset of the numbers in the sequence can be shown (except for short enough finite sequences, in which cases all terms can be shown).

For example, A000040 contains all positive primes in the unique factorization domain $\textstyle {\mathbb {Z} }$, but only the first sixty or so primes are listed in the main page for that sequence, while the b-file extends the listing range to the first hundred thousand primes.

The most obvious consequence of term visibility is its impact on searching. Returning to our example of the prime numbers, a search for "271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337" would fail to give A000040 as a search result (though it would probably appear in cross-references for the sequences that are returned as search matches). Hence it is preferable to search for smaller terms (though avoiding initial terms, since many otherwise identical sequences may have their first few terms distinct for different reasons.)

On a more whimsical line of thought, term visibility affects sequences that refer to other sequences listed in the OEIS and sequences that refer to themselves, such as A053873, "Numbers n such that OEIS sequence A_n contains n." For example, the term visibility of A000277 is currently limited to the first 53 terms, the fifty-third being 136, while 277 is the one hundred and fourth term. Therefore 277 is a term in A053873. However, for this purpose, sequences with keyword:dead are considered to contain only the terms shown.