6931467.646716369
6931468.33986355
6931469.0330107305
6931469.726157911
6931470.419305092
6931471.112452272
3465734.169931768
3465734.8630789486
3465735.5562261306
3465736.24937331
3465736.94252049
3465735.209652544
3465735.209652544
3465735.5562261483
3465735.9027997246
3465735.902799725
3465734.516505364
3465735.209652544
3465735.209652544
3465735.9027997246
3465735.902799725
3465736.595946905
3465735.2096525617
3465735.9027997428
SELECT max(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    number % 2,
    number % 3,
    ((number % 2) + (number % 3)) % 2
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY number % 5
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    (number % 2) * (number % 3),
    number % 3
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    number % 3,
    number % 2
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    (number % 2) % 3,
    number % 2
ORDER BY k ASC
6931467.646716369
6931468.33986355
6931469.0330107305
6931469.726157911
6931470.419305092
6931471.112452272
3465734.169931768
3465734.8630789486
3465735.5562261306
3465736.24937331
3465736.94252049
3465735.209652544
3465735.209652544
3465735.5562261483
3465735.9027997246
3465735.902799725
3465734.516505364
3465735.209652544
3465735.209652544
3465735.9027997246
3465735.902799725
3465736.595946905
3465735.2096525617
3465735.9027997428
SELECT max(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    number % 2,
    number % 3,
    ((number % 2) + (number % 3)) % 2
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    number % 5,
    (number % 5) * (number % 5)
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    (number % 2) * (number % 3),
    number % 3
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    (number % 2) * (number % 3),
    number % 3,
    number % 2
ORDER BY k ASC
SELECT avg(log(2) * number) AS k
FROM numbers(10000000)
GROUP BY 
    (number % 2) % 3,
    number % 2
ORDER BY k ASC