What number comes next? Ask the encyclopedia of correct sequences.

Some odd numbers:

1, 3, 5, 7, 9, 11, 13, 15…

some even:

2, 4, 6, 8, 10, 12, 14, 16…

Then there are the baffling “eban” numbers:

2, 4, 6, 30, 32, 34, 36, 40…

What number comes next? And why?

These are questions Neil Sloan, a mathematician in Highland Park, NJ, likes to ask. Dr. Sloan is the founder Online encyclopedia of correct sequences, a database consisting of 362,765 (and counting) numeric sequences defined by a specific rule or property. Like prime numbers:

2, 3, 5, 7, 11, 13, 17, 19…

Or Fibonacci numbers – each term (starting with the third term) is the sum of the two previous numbers:

0, 1, 1, 2, 3, 5, 8, 13…

This year OEIS, which has been praised As “the master indicator of mathematics” and “the mathematical equivalent of the FBI’s massive fingerprint files,” it celebrates its 50th anniversary. The original “Guide to Correct Sequences” collection appeared in 1973 and contains 2,372 entries. In 1995 it became an “encyclopedia” of 5487 sequences and an additional author, Simon Plouffe, a Quebec mathematician. A year later, the group had doubled in size again, so Dr. Sloan put it online.

“In a sense, every sequence is a puzzle,” Dr. Sloan said in a recent interview. He added that the puzzle aspect is incidental to the main purpose of the database: to systematize all mathematical knowledge.

Sequences are found in the wild – in mathematics, but also in quantum physics, genetics, communications, astronomy and in another place It can be confusing for many reasons. Searching for these entities in the OEIS, or adding them to the database, sometimes leads to enlightenment and discovery.

“It’s a source Unexpected resultssaid Lara Podwell, a mathematician at Valparaiso University in Indiana and a member of the OEIS Foundation Board of Trustees. Dr. Bodwell writes algorithms to solve counting problems. A few years ago, hence, I entered into the OEIS search box a sequence that arose while studying numerical patterns:

2, 4, 12, 20, 38, 56, 88…

The only result that stood out had to do with chemistry: specifically, the periodic table and the atomic numbers of the alkaline earth metals. “I found this baffling,” said Dr. Budwell. She consulted with chemists and soon “realized that there were interesting chemical combinations to work with to explain the connection.”