MathDB

Define a complexity of a set

a_1,a_2,\dots,

consisting of 0 and 1 to be the smallest positive integer

k

such that for some positive integers

\epsilon_1,\epsilon_2,\dots, \epsilon_k

each number of the sequence

a_n

n>k

, has the same parity as

\epsilon_1 a_{n-1}+\epsilon_2 a_{n-2}+\dots+\epsilon_k a_{n-k}

. Sequence

a_1,a_2,\dots,

has a complexity of

1000

. What is the complexity of sequence

1-a_1,1-a_2,\dots,

.
[I]Proposed by A. Kirichenko

Problem Statement