In 1964 Neil Sloane started the maintenance of a list of integer sequences. Once his collection grew, he published the list in a book in 1973 ("A Handbook of Integer Sequences", by NJAS, Academic Press, NY). This book contained 2372 sequences.
Since 1996. the list in the form of a database has been maintained on the internet. As of the date of this post, it has over 300,000 different sequences that can be searched in many different ways. The formal name is The On-Line Encyclopedia of Integer Sequences or OEIS. This is a link to the database.
The database is copyrighted by the OEIS Foundation, Inc.
Just to try out, I entered "1,2,3,4,5" in the search function. As expected, the first sequence listed was the positive integers (OEIS sequence identified as A000027). What I didn't expect was that there were 6820 other sequences that begin "1,2,3,4,5."
Many famous sequences are included such as the list of prime numbers, A00040, the Fibonacci numbers, A000045, and Pascal's triangle, A007318.
3-16-2021 Update.
I suggest viewing Mathologer YouTube entry on "What Comes Next?"
Also, view these Numberphile videos showing some of these sequences graphed:
3-26-2023 Update: My proposed sequence was published in the OEIS - A361746 - OEIS.
To view any of the sequences that I've authored or to which I have contributed, see: james c. mcmahon - OEIS.
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