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A352260 Integers that need 2 iterations of the map x->A352172(x) to reach 1.

%I A352260 #12 Mar 10 2022 17:33:37
%S A352260 25,52,125,152,205,215,250,251,455,502,512,520,521,545,554,1025,1052,
%T A352260 1125,1152,1205,1215,1250,1251,1455,1502,1512,1520,1521,1545,1554,
%U A352260 2005,2015,2050,2051,2105,2115,2150,2151,2255,2500,2501,2510,2511,2525,2552,4055,4155,4505
%N A352260 Integers that need 2 iterations of the map x->A352172(x) to reach 1.
%e A352260 25 -> 1000 -> 1.
%t A352260 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[4505], q[#, 2] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352260 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352260 isok2(n) = {for (k=1, 2, n = f(n); if ((n==1), return(k==2)););}
%o A352260 (Python)
%o A352260 from math import prod
%o A352260 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352260 def ok(x):
%o A352260     x = A352172(x)
%o A352260     return x != 1 and A352172(x) == 1
%o A352260 print([k for k in range(4506) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352260 Cf. A352172. Subsequence of A351876.
%Y A352260 Cf. A352261, A352262, A352263, A352264, A352265, A352266, A352267, A352268.
%K A352260 nonn,base
%O A352260 1,1
%A A352260 _Michel Marcus_, Mar 10 2022