SELECT 
  category_id, 
  parent_id 
FROM 
  categories 
WHERE 
  parent_id IN(
    13259, 13253, 13247, 7687, 13250, 13248, 
    13257, 13256, 13260, 13255, 13249, 
    13251, 13254, 7208, 13246, 10933, 13258, 
    13245, 13252, 13261, 10953
  )

Query time 0.00088

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "6.85"
    },
    "table": {
      "table_name": "categories",
      "access_type": "range",
      "possible_keys": [
        "parent"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 31,
      "rows_produced_per_join": 31,
      "filtered": "100.00",
      "using_index": true,
      "cost_info": {
        "read_cost": "3.75",
        "eval_cost": "3.10",
        "prefix_cost": "6.85",
        "data_read_per_join": "81K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "(`goimagine`.`categories`.`parent_id` in (13259,13253,13247,7687,13250,13248,13257,13256,13260,13255,13249,13251,13254,7208,13246,10933,13258,13245,13252,13261,10953))"
    }
  }
}

Result

category_id parent_id
7211 7208
13247 13246
13248 13246
13249 13246
13250 13246
13251 13246
13260 13246
13253 13252
13254 13252
13255 13252
13256 13252
13257 13252
13259 13252