  We characterize those strings whose suffix arrays are based on arithmetic
progressions, in particular, arithmetically progressed permutations where all
pairs of successive entries of the permutation have the same difference modulo
the respective string length. We show that an arithmetically progressed
permutation $P$ coincides with the suffix array of a unary, binary, or ternary
string. We further analyze the conditions of a given $P$ under which we can
find a uniquely defined string over either a binary or ternary alphabet having
$P$ as its suffix array. For the binary case, we show its connection to lower
Christoffel words, balanced words, and Fibonacci words. In addition to solving
the arithmetically progressed suffix array problem, we give the shape of the
Burrows-Wheeler transform of those strings solving this problem. These results
give rise to numerous future research directions.
