  In this paper, we consider a certain variation of the "isoperimetric problem"
adopted for subsets of nonnegative integers. More specifically, we explore the
sequence P(n) as described in OEIS A186053. We provide the first exact formulas
for P(n) including multiple recursive relations involving auxiliary functions
as well as concise and satisfying representations and quasi-explicit formulas.
We also discuss some of the intricate fractal-like symmetry of the sequence as
well as the development of algorithms for computing P(n). We conclude with open
questions for further research.
