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%I #13 Mar 10 2022 17:33:03
%S 55,155,505,515,550,551,1055,1155,1505,1515,1550,1551,2555,5005,5015,
%T 5050,5051,5105,5115,5150,5151,5255,5500,5501,5510,5511,5525,5552,
%U 10055,10155,10505,10515,10550,10551,11055,11155,11505,11515,11550,11551,12555,15005,15015,15050
%N Integers that need 10 iterations of the map x->A352172(x) to reach 1.
%e 55 -> 15625 -> 27000000 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
%t f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[15050], q[#, 10] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o isok10(n) = {for (k=1, 10, n = f(n); if ((n==1), return(k==10)););}
%o (Python)
%o from math import prod
%o def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o def ok(x, iters=10):
%o i = 0
%o while i < iters and x != 1: i, x = i+1, A352172(x)
%o return i == iters and x == 1
%o print([k for k in range(15051) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y Cf. A352172. Subsequence of A351876.
%Y Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352266, A352267.
%K nonn,base
%O 1,1
%A _Michel Marcus_, Mar 10 2022