

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.


0



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



