REU: Research Challenges of Identifying Integer Sequences Using the OEIS

The full 2016 Cohort up a tree.


The Mathematics and Computer Science Department of Muhlenberg College invites applications for a NSF Research Experiences for Undergraduates (REU) program in the summer (May 29 -- July 27) of 2018 that will concentrate on research projects associated with the On-Line Encyclopedia of Integer Sequences® (OEIS®) and its role in stimulating new research. Sequences play an important role in number theory, combinatorics and discrete mathematics, among many other fields. They enumerate objects in sets and define relationships among items or properties shared between them. Integer sequences have inspired mathematicians for centuries. By gathering sequences – and a wealth of information about them – together in a common database, the OEIS provides the mathematically curious an invaluable resource with which to explore. A particular emphasis of our program will be to discuss the important role the OEIS has played in developing conjectures in areas that include number theory, algorithmic and enumerative combinatorics, combinatorial number theory, and many other mathematical fields, as well as the tools necessary for identifying such conjectures.

Students will work in integrated teams with mentors and immerse themselves in open-ended mathematics research projects. Participating students will be provided a stipend of $4,500, on-campus housing with support for a summer meal plan, and travel expenses to and from the Muhlenberg College campus. Students will be assigned to research teams based on their interests and each team will be mentored by two faculty advisors. In addition to working on their collaborative projects, students will attend seminars, give presentations, and enjoy fun social activities. They will be encouraged to attend and give presentations at their home institutions as well as local and national professional meetings.

Muhlenberg College is part of the Lehigh Valley Association of Independent Colleges (LVAIC) community located in Allentown, PA. The LVAIC consortium is one of the oldest in the country consisting of six member institutions (Lehigh University, Muhlenberg College, Moravian College, DeSales University, Cedar Crest College, and Lafayette College) and six associate member institutions (Albright College; Alvernia University; Lehigh Carbon Community College; Neumann University; Northampton Community College; Reading Area Community College).


Application Process:

The program entails nine weeks of intensive work during the summer; student participants are strongly encouraged to continue their projects during the following academic year. Because of the nine-week intensive effort and on-site participation, students should not commit to other activities (e.g., courses) during the REU program. We expect the program will select ten undergraduates to participate. Supplemental funding may allow for selecting an additional 5 to 8 undergraduate participants. Participants will have LVAIC faculty members and/or OEIS assitant editors as supervisors. 

To submit your online application, go to the application process page for instructions on application guidelines and required application materials. Applications will be submitted through Click on the link for " Program applicant", create an account, and follow the directions at our program's listing. Applicants should be undergraduates with a major in Mathematics, Computer Science, or a closely related STEM field. They should be current sophomores or juniors, although first year students with exceptionally strong backgrounds will be considered. In exceptional circumstances, seniors will be allowed into the program if they will not have graduated by the time the program begins. Preference will be given to students who will continue their research projects during the academic year, under the direction of either their supervisor or a faculty member from their home institution. Due to funding agency rules, only U.S. Citizens and Permanent Residents who will be full time undergraduate students in Fall 2018 are eligible for funding support. Women, minorities, and students with disabilities are encouraged to apply.

If you would like more information about the program, the supervisors, or suggested research projects, please contact the REU Coordinators Dr. Eugene Fiorini (eugenefiorini at muhlenberg dot edu) or Dr. Byungchul Cha (cha at muhlenberg dot edu) or call 484-664-3299.


A Brief History of the OEIS:

The entire 2016 REU cohort in front of the Muhlenberg Man.

By gathering sequences – and a wealth of information about them – together in a common database, the OEIS provides the mathematically curious an invaluable resource with which to explore. It all began in 1964 when Neil Sloane was a graduate student at Cornell working on his dissertation. He happened upon a sequence that began with 0, 1, 8, 78, 944, which later became entry A000435 in the OEIS. To keep track of this and other sequences, he began recording them on index cards sorted in lexicographic order. By 1967 the sequences were transferred to punched cards, and in 1973 they were published in a book, A Handbook of Integer Sequences. The original edition contained 2,372 sequences. Almost immediately, Sloane began receiving correspondences from all over the world with suggestions for additional sequences and updates to existing ones. Over the next twenty years the collection continued to grow, leading to the publication of The Encyclopedia of Integer Sequences, a revised edition of the original book containing 5,487 sequences and coauthored with Simon Plouffe. Once again, suggestions poured in as soon as the new edition appeared in print. In 1996, Sloane launched The On-Line Encyclopedia of Integer Sequences, initially part of his homepage at AT&T Research until 2009 when the decision was made to set up a non-profit foundation, The OEIS Foundation Inc, to own and operate the OEIS. When the database went online it had approximately 10,000 sequences. Liberated from the space and distribution constraints imposed by print media, the OEIS is now growing at a rate of roughly 15,000 entries per year and currently has over 250,000 entries. Each entry typically contains a variety of useful information – the initial terms of the sequence, formulas, references, relevant links, Maple or Mathematica programs to generate it, etc. – harvested from a crowd of trusted contributors. The OEIS has become an invaluable resource for researchers and recreationalists alike, and it exemplifies the spirit of “if you build it they will come.” It was recently calculated that the OEIS database and related wiki get roughly 9 million page views per month – a true testament to the popularity of the OEIS. 

Click here for a pdf version of our 2018 REU flyer.

Funding for this program is generously provided by the National Science Foundation (NSF-DMS 1560019).