Many of my projects require extensive computations. This page is meant as a repository for various visualizations that I have created to help study various objects of interest, and for code for others to do the same. (At some point, I need to get around to cleaning up this code and maybe constructing a basic UI. In the meantime, I am generally happy to answer questions about these things work.)

## Integral Crystallographic Packings:

• Sage code for constructing super-packings and integral crystallographic packings: GitHub link
• Full table of super-packings and integral crystallographic packings can be found here: Table of sphere packings with remarks.
• Individual super-packings can be found here:
• Individual integral crystallographic packings can be found here:

## Ulam Sequences:

• Python code for computing elements of Ulam sequences U(1,n)GitHub link
• Python code for computing coefficients a_i, b_i, c_i, d_i such that U(1,n) = [a_0 n + b_0, c_0 n + d_0 n] ∪ [a_1 n + b_1, c_1 n + d_1 n] ∪ … by computing the integer polynomial Ulam sequence U(1,X)GitHub link
• Python code for computing coefficients a_i, b_i, c_i, d_i such that U(1,n) = [a_0 n + b_0, c_0 n + d_0 n] ∪ [a_1 n + b_1, c_1 n + d_1 n] ∪ … given Ulam sequences U(1,2), U(1,3),… U(1,14). Currently has all coefficients up to (a_217529, b_217529, c_217529, d_217529 ) = (966409, 134342, 966410, 134340)GitHub link