Some numbers are odd:
1, 3, 5, 7, 9, 11, 13, 15…
Some are even:
2, 4, 6, 8, 10, 12, 14, 16…
And then there’s also the cryptic “eban” numbers.
2, 4, 6, 30, 32, 34, 36, 40…
What’s the next number? why?
These are questions that mathematician Neil Sloan of Highland Park, New Jersey likes to ask. Dr. Sloane Online Encyclopedia of Integer Sequences, a database of 362,765 (and growing) numeric sequences defined by precise rules or properties. Prime numbers, etc.:
2, 3, 5, 7, 11, 13, 17, 19…
Or Fibonacci numbers — every term (starting with the third term) is the sum of the two preceding numbers.
0, 1, 1, 2, 3, 5, 8, 13…
This year’s OEIS admired It celebrates its 50th anniversary as the “master index of mathematics” and “mathematical equivalent of the FBI’s enormous fingerprint file.” His original collection, A Handbook of Integer Sequences, was published in 1973 and contained 2,372 items. In 1995, the book became an “encyclopedia” containing his 5,487 sequences and the additional authorship of Quebec mathematician Simon Plouffe. A year later, when the collection had doubled in size again, Dr. Sloan published it on the Internet.
“In a way, every sequence is a puzzle,” Dr. Sloan said in a recent interview. He added that the puzzle aspect is incidental to the database’s primary purpose of organizing all mathematical knowledge.
Sequences of numbers that exist in nature, not only in mathematics, but also in quantum physics, genetics, communications, astronomy, etc. elsewhere — can be cryptic for a variety of reasons. Searching for these entities in OEIS or adding them to the database can lead to enlightenment and discovery.
“that is, unexpected resultsaid a mathematician at the University of Valparaiso, Indiana, of the OEIS Foundation Board of Trustees. Dr. Padwell creates an algorithm that solves counting problems. A few years ago, she tackled this by typing into the OEIS search box any sequence that came to mind while studying numerical patterns.
2, 4, 12, 20, 38, 56, 88…
The only results that emerged were related to chemistry, specifically the periodic table and the atomic numbers of the alkaline earth metals. “This puzzled me,” said Dr. Padwell. She consulted a chemist and soon “realized that there was an interesting chemical structure to explain the connection.”
