Some numbers are odd:

### 1, 3, 5, 7, 9, 11, 13, 15 …

Some are even:

### 2, 4, 6, 8, 10, 12, 14, 16 …

After which there are the puzzling “eban” numbers:

### 2, 4, 6, 30, 32, 34, 36, 40 …

What quantity comes subsequent? And why?

These are questions that Neil Sloane, a mathematician of Highland Park, N.J., likes to ask. Dr. Sloane is the founding father of the On-Line Encyclopedia of Integer Sequences, a database of 362,765 (and counting) quantity sequences outlined by a exact rule or property. Such because the prime numbers:

### 2, 3, 5, 7, 11, 13, 17, 19 …

Or the Fibonacci numbers — each time period (beginning with the third time period) is the sum of the 2 previous numbers:

### 0, 1, 1, 2, 3, 5, 8, 13 …

This yr the OEIS, which has been praised as “the grasp index to arithmetic” and “a mathematical equal to the FBI’s voluminous fingerprint information,” celebrates its fiftieth anniversary. The unique assortment, “A Handbook of Integer Sequences,” appeared in 1973 and contained 2,372 entries. In 1995, it grew to become an “encyclopedia,” with 5,487 sequences and an extra writer, Simon Plouffe, a mathematician in Quebec. A yr later, the gathering had doubled in measurement once more, so Dr. Sloane put it on the web.

“In a way, each sequence is a puzzle,” Dr. Sloane stated in a latest interview. He added that the puzzle facet is incidental to the database’s essential function: to arrange all mathematical information.

Sequences discovered within the wild — in arithmetic, but additionally quantum physics, genetics, communications, astronomy and elsewhere — could be puzzling for quite a few causes. Trying up these entities within the OEIS, or including them to the database, typically results in enlightenment and discovery.

“It’s a supply of surprising outcomes,” stated Lara Pudwell, a mathematician at Valparaiso College in Indiana and a member of the OEIS Basis’s board of trustees. Dr. Pudwell writes algorithms to unravel counting issues. A number of years in the past, thus engaged, she entered into the OEIS search field a sequence that arose whereas finding out numerical patterns:

### 2, 4, 12, 20, 38, 56, 88 …

The one outcome that popped up pertained to chemistry: particularly, to the periodic desk and the atomic numbers of the alkaline earth metals. “I discovered this perplexing,” Dr. Pudwell stated. She consulted with chemists and shortly “realized there have been fascinating chemical buildings to work with to elucidate the connection.”