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

1,1

Comments

f(x) = A352598(x).

Fixed points of f(x) are in A115385.

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

Links

Table of n, a(n) for n=1..15.

Example

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

Prog

(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)))

Crossrefs

Subsequence of the intersection of A000290 and A002473.

Cf. A115385, A351327, A352598.

Sequence in context: A217848 A044872 A044979 * A345534 A345786 A186473

Adjacent sequences: A352592 A352593 A352594 * A352596 A352597 A352598

Keyword

nonn,base,more

Author

Michael S. Branicky, Mar 24 2022

Status

approved