oeis-search

This is a script to perform complex searches on the OEIS database. When run, it will prompt you to enter a search (see the Syntax section below), and will display any sequences that match the search (capped at 10 by default, but this can be altered in the code easily).

Instructions

• Download each of the two compressed files given here at the OEIS.
• Decompress the files, which should have default filenames of names and stripped.
• Rename these files to names.txt and stripped.txt respectively.
• Put these two files in the same folder as the oeis.py file.
• Run oeis.py, at which point you will be prompted to enter a search.

Syntax

Some progressively more complicated searches, and the conditions they impose on a sequence:

• 1, 2, 3, 4: Sequence must start with those four terms in that order.
• 0?, 1, 2, 3, 4: Sequence must start with either 0, 1, 2, 3, 4 or 1, 2, 3, 4 (i.e., the 0 is optional).
• 1, 3, 5, 7|8, 10: Fourth term is either 7 or 8 (along with the other specified terms).
• even, even, odd, prime: First term is even, second term is even, third term is odd, fourth term is prime.
• 1, 2, 3, (4 | prime): Fourth term is either 4 or a prime.
• 1, 1, 2, 5, 10-15, >, >=,: Fifth term is between 10 and 15 inclusive, the sixth term is strictly greater than the fifth, and the seventh term is greater than or equal to the sixth.
• 2, 4, 2, prime*: All terms after the third term are prime.
• 3%4, 5%7, (3%5 & <=)*: First term is congruent to 3 mod 4, second term is congruent to 5 mod 7, all subsequent terms are congruent to 3 mod 5 and less than or equal to the previous term.
• 3*, 5, 7*: Sequence consists of some nonnegative number of 3s, followed by a 5, followed by some nonnegative number of 7s.
• *, 10, 3, 4: Sequence contains the terms 10, 3, 4 in order consecutively, but not necessarily at the start.
• *, 10, *, 3, *, 4: Sequence contains the terms 10, 3, 4 in order, but not necessarily consecutively.
• 1, 3, 8, _, 11: There is a fourth term between 8 and 11, but it could be anything.
• 1, 3, 8, (!=3)?, 11: There might or might not be a term between 8 and 11, but if there is, it isn't 3.
• _, (!prime & >1)*: All terms after the first are composite.

The parser supports nested parentheses, if you want to use more complex logic.

This syntax allows for computationally costly queries (things with a lot of question marks especially), so some searches may take a while to complete, but for most normal use cases, a search should terminate in under 10 seconds at most, and usually within a second. The prime keyword defaults to the Miller-Rabin probabilistic primality test for inputs over 100 million.