A352595 Positive integers that are fixed points for the map x->f^k(x) for some k>1, where f(x) is the product of squares of nonzero digits of x.

256, 324, 576, 3600, 11664, 15876, 20736, 44100, 63504, 65536, 129600, 2822400, 5308416, 7290000, 8294400

Offset: 1

Author

Michael S. Branicky, Mar 24 2022

Keywords

• nonn
• base
• more

Comments

f(x) = A352598(x).

Fixed points of f(x) are in A115385.

64524128256, 386983526400, 849346560000, 49787136000000, 55725627801600 are also terms.

Examples

			256 -> 3600 -> 324 -> 576 -> 44100 -> 256 is a limit cycle of f, so all elements are terms.
		

Crossrefs

Subsequence of the intersection of A000290 and A002473.

Cf. A115385, A351327, A352598.

Programs

Python

from math import prod
from itertools import count, islice
def f(n): return prod(int(d)**2 for d in str(n) if d != "0")
def ok(n):
    n0, k, seen = n, 0, set(),
    while n not in seen: # iterate until fixed point or in cycle
        seen.add(n)
        n = f(n)
        k += 1
    return n == n0 and k > 1
def agen(startk=1):
    for m in count(1):
        if ok(m): yield m
print(list(islice(agen(), 11)))