cp's OEIS Frontend

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.

%I A352595 #8 Mar 26 2022 14:50:11
%S A352595 256,324,576,3600,11664,15876,20736,44100,63504,65536,129600,2822400,
%T A352595 5308416,7290000,8294400
%N 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.
%C A352595 f(x) = A352598(x).
%C A352595 Fixed points of f(x) are in A115385.
%C A352595 64524128256, 386983526400, 849346560000, 49787136000000, 55725627801600 are also terms.
%e A352595 256 -> 3600 -> 324 -> 576 -> 44100 -> 256 is a limit cycle of f, so all elements are terms.
%o A352595 (Python)
%o A352595 from math import prod
%o A352595 from itertools import count, islice
%o A352595 def f(n): return prod(int(d)**2 for d in str(n) if d != "0")
%o A352595 def ok(n):
%o A352595     n0, k, seen = n, 0, set(),
%o A352595     while n not in seen: # iterate until fixed point or in cycle
%o A352595         seen.add(n)
%o A352595         n = f(n)
%o A352595         k += 1
%o A352595     return n == n0 and k > 1
%o A352595 def agen(startk=1):
%o A352595     for m in count(1):
%o A352595         if ok(m): yield m
%o A352595 print(list(islice(agen(), 11)))
%Y A352595 Subsequence of the intersection of A000290 and A002473.
%Y A352595 Cf. A115385, A351327, A352598.
%K A352595 nonn,base,more
%O A352595 1,1
%A A352595 _Michael S. Branicky_, Mar 24 2022