SELECT 
  category_id, 
  parent_id 
FROM 
  jmj_categories 
WHERE 
  parent_id IN(
    31, 32, 33, 34, 35, 37, 38, 39, 41, 40, 43, 
    42, 44
  ) 
  AND category_id != 1

Query time 0.01100

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "31.21"
    },
    "table": {
      "table_name": "jmj_categories",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 13,
      "rows_produced_per_join": 13,
      "filtered": "100.00",
      "index_condition": "(`jmj_test`.`jmj_categories`.`parent_id` in (31,32,33,34,35,37,38,39,41,40,43,42,44))",
      "cost_info": {
        "read_cost": "28.61",
        "eval_cost": "2.60",
        "prefix_cost": "31.21",
        "data_read_per_join": "50K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "(`jmj_test`.`jmj_categories`.`category_id` <> 1)"
    }
  }
}