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Some odd numbers:
1, 3, 5, 7, 9, 11, 13, 15…
Some even:
2, 4, 6, 8, 10, 12, 14, 16…
And then there are the surprising “eban” numbers:
2, 4, 6, 30, 32, 34, 36, 40…
What’s the next number? And why?
This is the question that Neil Sloane, a mathematician from Highland Park, NJ, loves to ask. Dr. Sloane is the founder of the On-Line Encyclopedia of Integer Sequences, a database of 362,765 (and counting) number sequences defined by precise rules or properties. For example prime numbers:
2, 3, 5, 7, 11, 13, 17, 19…
Or Fibonacci numbers – each term (starting with term 3) is the sum of the previous two numbers:
0, 1, 1, 2, 3, 5, 8, 13…
This year the OEIS, hailed as “the master index for mathematics” and “the mathematical equivalent of the vast FBI fingerprint file,” celebrates its 50th anniversary. The original collection, “A Handbook of Integer Sequences,” appeared in 1973 and contains 2,372 entries. In 1995, it became an “encyclopedia,” with 5,487 entries and an additional author, Simon Plouffe, a mathematician in Quebec. A year later, the collection has doubled, so Dr. Sloane put it on the internet.
“In a sense, each sequence is a puzzle,” said Dr. Sloane in a recent interview. He adds that the puzzle aspect is irrelevant to the main purpose of the database: to organize all mathematical knowledge.
The order found in the wild – in mathematics, but also quantum physics, genetics, communication, astronomy and more – can be surprising for many reasons. Searching for these entities in the OEIS, or adding them to the database, sometimes leads to enlightenment and discovery.
“This is a source of unexpected results,” said Lara Pudwell, a mathematician at Valparaiso University in Indiana and a member of the OEIS Foundation’s board of trustees. Dr. Pudwell wrote an algorithm to solve counting problems. A few years ago, thus participating, he entered in the search box OEIS the sequence that appeared when studying numerical patterns:
2, 4, 12, 20, 38, 56, 88…
The only results that emerged were in chemistry: specifically, for the periodic table and the atomic number of the alkaline earth metals. “I find this confusing,” said Dr. Pudwell. He consulted a chemist and soon “knew there was an interesting chemical structure to work with to explain the relationship.”
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