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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 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.)