A352595 - OEIS

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

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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

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.

KEYWORD

nonn,base,more

AUTHOR

STATUS

approved