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 are the strangers:
0, 5, 4, 2, 9, 8, 6…
What number is next? And because?
These are questions that Neil Sloane, a mathematician in New Jersey, loves to ask. He is the founder of the Online Encyclopedia of Integer Sequences, or OEIS, a database of 362,765 (and counting) number sequences defined by a precise rule or property. Like the prime numbers:
2, 3, 5, 7, 11, 13, 17, 19…
Or the 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 the OEIS celebrates its 50th anniversary. The original collection, “A Handbook of Integer Sequences,” appeared in 1973 and contained 2,372 entries. In 1995, it became an “encyclopedia,” with 5,487 sequences and an additional author, Simon Plouffe, a mathematician from Quebec. A year later, the collection had doubled in size, so Sloane put it online.
“In a sense, each sequence is a puzzle,” Sloane said, adding that the main purpose of the database is to organize all mathematical knowledge.
Sequences found in mathematics, quantum physics, genetics, communications, astronomy, and elsewhere can be puzzling for a number of reasons. Searching for these entities in the OEIS, or adding them to the database, sometimes leads to enlightenment and discovery.
“It’s a source of unexpected results,” said Lara Pudwell, a mathematician at Valparaiso University in Indiana and a board member of the OEIS Foundation. A few years ago, she captured in the OEIS a sequence that arose while studying number patterns: 2, 4, 12, 20, 38, 56, 88…
The only result that appeared was for the periodic table and the atomic numbers of the alkaline earth metals. “I found that disconcerting,” he said. He consulted with chemists and soon realized “that there were interesting chemical structures to work with to explain the connection.”
The OEIS contains many teasing and joke-like sequences, such as the bizarre sequence mentioned at the beginning of this text.
The joke is that the number 7 follows, because the numbers are in alphabetical order.
Sloane first searched for a sequence in 1964, when she was a graduate student. By studying paths in an artificial neural network, his calculations generated:
0, 1, 8, 78, 944, 13800…
“I urgently needed a formula for the nth term to determine the growth rate of terms,” he wrote in a retrospective published in April. “This would indicate how long activity would persist in this very simple neural network.” Searching books and journals, he came close, but found no sequence. Finally, with the combinatorialist John Riordan, he discovered the formula and the following term: 237432.
Along the way, Sloane jotted down sequences on file cards and then on punched cards. In 1995, the OEIS went online, in 2010 it became a moderated wiki, and is now run by some 170 international volunteer editors who scrutinize 50 or more new applicants a day.
Sloane showcases her favorite sequences on Numberphile, a YouTube channel, always asking “What number is next?” Among her current favorites of hers is the Sisyphus sequence, devised in 2022 by Éric Angelini, an amateur journalist and mathematician from Brussels, and her sometime accomplice, Carole Dubois, from Toulouse, France.
1, 3, 6, 3, 8, 4, 2, 1…
Sisyphus Rule: If the number is even, divide by two. If the number is odd, add the smallest prime number that hasn’t been added yet. The first term, 1, is odd, so adding the smallest prime number, 2, gives 3; 3 is odd, so adding the next prime number, 3, gives you 6; 6 is even, so dividing by two gives 3, and so on.
“Now here’s the interesting question,” said Sloane: some numbers appear more than once, but do all numbers appear at least once? “We do not know”.
By: SIOBHAN ROBERTS
BBC-NEWS-SRC: http://www.nytsyn.com/subscribed/stories/6740823, IMPORTING DATE: 2023-06-01 18:20:09
#giant #database #number #sequences #whats