Seleccionar valores de una lista que no están en una tabla

Una tabla temporal es la mejor solución, pero si no es posible, puede modificar una tabla temporal seleccionando constantes y uniéndolas.

Usando esta solución puede hacer lo siguiente:-

SELECT i
FROM 
(
    SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 6 UNION SELECT 7
) AS mylistofids 
LEFT JOIN mytable
ON mytable.id = i
WHERE mytable.id IS NULL;

También puede generar un rango masivo de números (asumiendo que está tratando con ID de números enteros) al unir rangos de números. Luego, simplemente elija los que están en la cláusula IN:-

SELECT i
FROM 
(
    SELECT units.i + tens.i * 10 + hundreds.i * 100 + thousands.i * 1000 + tensthousands.i * 10000 AS i
    FROM (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS units
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS tens
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS hundreds
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS thousands
    CROSS JOIN (SELECT 1 AS i UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9 UNION SELECT 0 ) AS tensthousands
) AS mylistofids 
LEFT JOIN mytable
ON mytable.id = i
WHERE mylistofids.i IN (1, 2, 3, 6, 7)
AND mytable.id IS NULL;