User:Georg Fischer/Coincidences

The goal of this small project is to scan for coincidences in the terms of pairs of sequences.

I wrote a Perl program and a companion makefile. My procedure is as follows:

1. Fetch the files stripped.gz and names.gz.
2. Start at any term >= 4 and sort by those subsequences.
3. Ignore subsequences shorter than 6 terms. Also ignore subsequences consisting of single digit terms only.
4. In blocks of 50000 sequences, examine all pairs where one subsequence is the beginning of the other.
5. Exclude sequences with the strings "McKay-Thompson series", " Weyl group " or "Coxeter" in the name.
6. For such pairs, read the sequence descriptions with &fmt=text and a delay of 8 s per file.
7. Check whether the lower (older) sequence number is mentioned in the higher (newer) sequence description and vice versa, and set colors (ok, warning). A candidate has a yellow line for the newer sequence.
8. Examine the resulting HTML file, and select "interesting" candidates manually.

It was only during this process when I saw that Richard Mathar had already cared for most of the cases. Nevertheless, some dozens of the sequences per block could still be examined.

A lot of changes were initiated by these lists in October 2018. Now I regenerate them only occasionally:

Overview with counts
A000000-A049999
A050000-A099999
A100000-A149999
A150000-A199999
A200000-A249999
A250000-A299999
A300000-A349999
A350000-A399999

Highlights

• Neil's posting to the Seqfan email list "Two questions looking for answers" of 25 Oct. 2018 and mentioned in his talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Nov. 15 2018: video (Part 2), at 18:50', and slides (PDF)

A045318 Primes p such that x^8 = 3 has no solution mod p.
A301916 Primes which divide numbers of the form 3^k + 1.

A027595 and A007212