Postgres 16

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SELECT *
FROM   generate_series(timestamp '2023-10-21 00:00'
                     , timestamp '2023-10-21 00:25'
                     , interval '15 min')
ORDER BY 1;  -- optional

generate_series

2023-10-21 00:00:00

2023-10-21 00:15:00

SELECT 2

-- get ceiling for end value with date_bin()
SELECT date_bin(interval '15 min'
              , timestamp '2023-10-21 00:25'
              , timestamp '2023-10-21 00:00') + interval '15 min';

?column?

2023-10-21 00:30:00

SELECT 1

-- fails for exact step
SELECT generate_series(a, date_bin(intv, z, a) + intv, intv)
FROM  (
   VALUES (timestamp '2023-10-21 00:00'
         , timestamp '2023-10-21 00:25'
         , interval '15 min')
   ) input(a, z, intv);

generate_series

2023-10-21 00:00:00

2023-10-21 00:15:00

2023-10-21 00:30:00

SELECT 3

-- works: increment unless we hit the interval
SELECT generate_series(a, CASE WHEN date_bin(intv, z, a) = z THEN z ELSE date_bin(intv, z, a) + intv END, intv)
FROM  (
   VALUES (timestamp '2023-10-21 00:00'
         , timestamp '2023-10-21 00:29'
         , interval '15 min')
   ) input(a, z, intv);

generate_series

2023-10-21 00:00:00

2023-10-21 00:15:00

2023-10-21 00:30:00

SELECT 3