proof

• 2n

  always even
• 2n-1

  odd
• 2n+1

  odd
• 3n

  multiple of 3
• n + 2

  consecutive number odd
• n + 1

  consecutive
• 2n + 1

  consecutive odd
• 2n + 3

  consecutive odd
• 2n + 5

  consecutive odd
• 2n

  consecutive even
• 2n + 2

  consecutive even
• 2n + 4

  consecutive even