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A352262 Integers that need 4 iterations of the map x->A352172(x) to reach 1.

%I A352262 #13 Mar 10 2022 17:32:52
%S A352262 2,12,20,21,45,54,102,112,120,121,145,154,200,201,210,211,225,252,405,
%T A352262 415,450,451,504,514,522,540,541,558,585,855,1002,1012,1020,1021,1045,
%U A352262 1054,1102,1112,1120,1121,1145,1154,1200,1201,1210,1211,1225,1252,1405,1415,1450,1451
%N A352262 Integers that need 4 iterations of the map x->A352172(x) to reach 1.
%e A352262 2 -> 8 -> 512 -> 1000 -> 1.
%t A352262 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[1451], q[#, 4] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352262 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352262 isok4(n) = {for (k=1, 4, n = f(n); if ((n==1), return(k==4)););}
%o A352262 (Python)
%o A352262 from math import prod
%o A352262 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352262 def ok(x, iters=4):
%o A352262     i = 0
%o A352262     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352262     return i == iters and x == 1
%o A352262 print([k for k in range(1452) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352262 Cf. A352172. Subsequence of A351876.
%Y A352262 Cf. A352260, A352261, A352263, A352264, A352265, A352266, A352267, A352268.
%K A352262 nonn,base
%O A352262 1,1
%A A352262 _Michel Marcus_, Mar 10 2022