-- SQL Query to Generate Fibonacci Numbers Up to the Largest Prime Number Below 2^5

-- Author: Ruslana Kruk

WITH Numbers AS (

-- Generate numbers from 1 to 32 (2^5)

SELECT LEVEL AS Numbb

FROM DUAL

CONNECT BY LEVEL <= POWER(2, 5)

),

Maxim AS (

-- Find the maximum prime number in the generated sequence

SELECT MAX(N1.Numbb) AS Maxx

FROM Numbers N1

WHERE NOT EXISTS (

-- Exclude numbers that are not prime

SELECT NULL

FROM Numbers N2

WHERE N1.Numbb > N2.Numbb

AND N2.Numbb <> 1

AND MOD(N1.Numbb, N2.Numbb) = 0

)

ORDER BY N1.Numbb

)

-- Calculate Fibonacci numbers up to the largest prime number below 32

SELECT ROUND((POWER((1 + SQRT(5)) / 2, Num1.Numbb) - POWER((1 - SQRT(5)) / 2, Num1.Numbb)) / SQRT(5)) AS Fib

FROM Numbers Num1

WHERE EXISTS (

-- Select only numbers less than the maximum prime number

SELECT *

FROM Maxim m

WHERE m.Maxx > Num1.Numbb

);