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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 11:14 EST 2022. Contains 358359 sequences. (Running on oeis4.)