Max. number of repeated square root operations in interval

# Maximum number of repeated square root operations in given interval.
import math as m
A = 6000 # A must not be 1 because then infinite operations can occur, sqrt(1) = 1
B = 7000
nops = 0
a = m.ceil(m.sqrt(A))
b = m.floor(m.sqrt(B))
while b >= a:
    a = m.ceil(m.sqrt(a))
    b = m.floor(m.sqrt(b))
    nops = nops + 1
print([A, B, nops])