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SELECT 
  category_id, 
  parent_id 
FROM 
  jmj_categories 
WHERE 
  parent_id IN(
    83, 104, 106, 69, 67, 68, 105, 70, 84, 82, 
    107, 85, 71, 108, 72, 86, 73, 74, 75, 76, 
    77
  ) 
  AND category_id != 1

Query time 0.01101

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "29.42"
    },
    "table": {
      "table_name": "jmj_categories",
      "access_type": "ALL",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "rows_examined_per_scan": 120,
      "rows_produced_per_join": 35,
      "filtered": "30.00",
      "cost_info": {
        "read_cost": "22.22",
        "eval_cost": "7.20",
        "prefix_cost": "29.42",
        "data_read_per_join": "139K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`jmj_test`.`jmj_categories`.`parent_id` in (83,104,106,69,67,68,105,70,84,82,107,85,71,108,72,86,73,74,75,76,77)) and (`jmj_test`.`jmj_categories`.`category_id` <> 1))"
    }
  }
}

Result

category_id	parent_id
83	68
69	67
104	82
106	82
70	67
84	68
105	82
71	67
85	68
107	82
72	67
86	68
108	82
73	67
74	67
75	67
76	67
77	67

category_id	parent_id
83	68
69	67
104	82
106	82
70	67
84	68
105	82
71	67
85	68
107	82
72	67
86	68
108	82
73	67
74	67
75	67
76	67
77	67

category_id	parent_id
83	68
69	67
104	82
106	82
70	67
84	68
105	82
71	67
85	68
107	82
72	67
86	68
108	82
73	67
74	67
75	67
76	67
77	67

category_id	parent_id
83	68
69	67
104	82
106	82
70	67
84	68
105	82
71	67
85	68
107	82
72	67
86	68
108	82
73	67
74	67
75	67
76	67
77	67