Kenneth Rosen Edition 7 Exercise 6.2 Question 21 (Page No. 406)

Question

Construct a sequence of $16$ positive integers that has no increasing or decreasing subsequence of five terms.

Answer 1

The sequence

${n+3,n+2,n +1,n,n + 7,n +6, n+5,n +4, n+11, n +10,n +9,n+8,n+ 15,n +14,n+ 13,n+12}$
it has both increasing and decreasing subsequences of maximum length 4.
Input $n = 1$.
RESULT
${4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13}$

Input $n = 2$.

RESULT

${5,4,3,2,9,8,7,6,13,12,11,10,17,16,15,14}$