Abstract A k‐extended q‐near Skolem sequence of order n, denoted by N n q ( k ), is a sequence s 1 , s 2 , … , s 2 n − 1 where s k = 0 and for each integer ℓ ∈ 1 , n { q } there are two indices i , j such that s i = s j = ℓ and ∣ i − j ∣ = ℓ. For a N n q ( k ) to exist it is necessary that q ≡ k ( mod 2 ) when n ≡ 0 , 1 ( mod 4 ) and q ≢ k ( mod 2 ) when n ≡ 2 , 3 ( mod 4 ), where ( n , q , k ) ≠ ( 3 , 2 , 3 ) , ( 4 , 2 , 4 ). Any triple ( n , q , k ) satisfying these conditions is called admissible. In this article, which is Part II of three articles, we construct sequences N n q ( k ) for all admissible ( n , q , k ) with q ∈ ⌊ n 2 ⌋ , n .
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