MathDB

A subset of the positive integers

S

is said to be a \emph{configuration} if 200

\notin S

and for all nonnegative integers

x

x \in S

if and only if both 2

x\in S

and

\left \lfloor{\frac{x}{2}}\right \rfloor\in S

. Let the number of subsets of

\{1, 2, 3, \dots, 130\}

that are equal to the intersection of

\{1, 2, 3, \dots, 130\}

with some configuration

S

equal

k

. Compute the remainder when

k

is divided by 1810.
Proposed Hari Desikan (HariDesikan)

Problem Statement