Here in the shadow of national Pi Day, it is a week in which to explore the world of numbers! What is your favorite number? What numbers are fascinating? What numbers are boring? You can’t tell me that the graphic above isn’t just as interesting as can be. Not only is it fascinating, I am equally intrigued by the person who spotted the sequence.

There are some numbers that are mysterious. Take author Douglas Adams’s popular 1979 science-fiction novel The Hitchhiker’s Guide to the Galaxy, the first in a series of five. Toward the end of the book, the supercomputer Deep Thought reveals that the answer to the “Great Question” of “Life, the Universe and Everything” is “forty-two.” And so started the great debate on the meaning of “42.” The author’s choice of the number 42 has become a fixture of geek culture. It’s at the origin of a multitude of jokes and winks exchanged between initiates. If, for example, you ask your search engine variations of the question “What is the answer to everything?” it will most likely answer “42.”  I just asked “Alexa” and sure enough she answered “42.”

The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out. For example: In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins. Also, the Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.” Just saying…some numbers are interesting.  …and for baseball fans, it was Jackie Robinson’s jersey number.

Back in 1963, while working on his doctorate in Mathematics, Neil Sloane, found his research into his doctoral thesis stymied by the lack of an easy way to see if other mathematicians had already done certain calculations. He came across a sequence of numbers: 0, 1, 8, 78, 944,… He did not yet know how to calculate the numbers in this sequence exactly and would have liked to know whether his colleagues had already come across a similar sequence during their research. But unlike logarithms or formulas, there was no registry for sequences of numbers. And so, 10 years later, Sloane published his first encyclopedia, A Handbook of Integer Sequences, which contained about 2,400 sequences that also proved useful in making certain calculations. It was soon to become the “go-to” resource for integer sequences.

In the years that followed, numerous submissions with more sequences reached Sloane, and scientific papers with new number sequences also appeared. Collaborating with Simon Plouffe, they published the  1995 first edition of The Encyclopedia of Integer Sequences , which contained some 5,500 sequences. The hardcopy version was great, but it limited the size of the sequences that could be described and made available. The number of entries grew exponentially as did the size of the sequences. Enter the internet. In 1996, the Online Encyclopedia of Integer Sequences (OEIS) appeared in a format unconstrained by any limitations on the number of sequences that could be recorded. As of March 2023, it contains just more than 360,000 entries.

Besides well-known sequences such as the prime numbers (2, 3, 5, 7, 11,…), powers of 2 (2, 4, 8, 16, 32,…) or the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13,…), the OEIS catalog also contains exotic examples such as the number of ways to build a stable tower from n two-by-four-studded Lego blocks, (1, 24, 1,560, 119,580, 10,166,403,…) or the “lazy caterer’s sequence” (1, 2, 4, 7, 11, 16, 22, 29,…), the maximum number of pie pieces that can be achieved by n cuts.

So, lest you think of a number as boring because it is not as famous as pi (π), Euler’s number (e) or the square root of 2, just enter that number into the OEIS database and discover its “hidden life.”

References:

• Manon Bischoff, “The Most Boring Number in the World Is … ”, Scientific America online March 2023 originally appeared in Spektrum der Wissenschaft.
• Jean-Paul Delahaye, “For Math Fans: A Hitchhiker’s Guide to the Number 42”, Scientific America online September 2020.