# Alternate Python programs for A378562
# Michael S. Branicky, Dec 03 2024

# For computing single values of a(n), up to very large n.

from sympy.ntheory import digits
def fd(t, b): return sum(t[-1-i]*b**i for i in range(len(t)))
def f(n): return next(fd(r, b) for b in range(2, n+1) if (s:=digits(n, b)[1:]) > (r:=s[::-1]))
def a(n):
    c = 0
    while n != 1: c += 1; n = f(n)
    return c

# Example usage:
print(a(10**1000))



# Faster for initial segment of sequence; uses code above.

from itertools import count, islice
def agen(): # generator of terms
    alst = [None, 0]
    for n in count(2):
        yield alst[-1]
        alst.append(1 + alst[f(n)])

# Example usage:

print(list(islice(agen(), 10**6)))