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A352265 Integers that need 7 iterations of the map x->A352172(x) to reach 1.

%I A352265 #11 Mar 10 2022 17:33:20
%S A352265 478,487,748,784,847,874,1478,1487,1748,1784,1847,1874,2278,2287,2447,
%T A352265 2474,2728,2744,2782,2827,2872,4078,4087,4178,4187,4247,4274,4427,
%U A352265 4472,4708,4718,4724,4742,4780,4781,4807,4817,4870,4871,5788,5878,5887,7048,7084,7148,7184,7228
%N A352265 Integers that need 7 iterations of the map x->A352172(x) to reach 1.
%e A352265 478 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
%t A352265 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[7228], q[#, 7] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352265 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352265 isok7(n) = {for (k=1, 7, n = f(n); if ((n==1), return(k==7)););}
%o A352265 (Python)
%o A352265 from math import prod
%o A352265 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352265 def ok(x, iters=7):
%o A352265     i = 0
%o A352265     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352265     return i == iters and x == 1
%o A352265 print([k for k in range(7229) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352265 Cf. A352172. Subsequence of A351876.
%Y A352265 Cf. A352260, A352261, A352262, A352263, A352264, A352266, A352267, A352268.
%K A352265 nonn,base
%O A352265 1,1
%A A352265 _Michel Marcus_, Mar 10 2022