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A352263 Integers that need 5 iterations of the map x->A352172(x) to reach 1.

%I A352263 #11 Mar 10 2022 17:33:32
%S A352263 679,697,769,796,967,976,1679,1697,1769,1796,1967,1976,2379,2397,2739,
%T A352263 2793,2937,2973,3279,3297,3367,3376,3637,3673,3729,3736,3763,3792,
%U A352263 3927,3972,6079,6097,6179,6197,6337,6373,6709,6719,6733,6790,6791,6907,6917,6970,6971,7069,7096
%N A352263 Integers that need 5 iterations of the map x->A352172(x) to reach 1.
%e A352263 679 -> 54010152 -> 8000000 -> 512 -> 1000 -> 1.
%t A352263 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[7096], q[#, 5] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352263 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352263 isok5(n) = {for (k=1, 5, n = f(n); if ((n==1), return(k==5)););}
%o A352263 (Python)
%o A352263 from math import prod
%o A352263 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352263 def ok(x, iters=5):
%o A352263     i = 0
%o A352263     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352263     return i == iters and x == 1
%o A352263 print([k for k in range(7100) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352263 Cf. A352172. Subsequence of A351876.
%Y A352263 Cf. A352260, A352261, A352262, A352264, A352265, A352266, A352267, A352268.
%K A352263 nonn,base
%O A352263 1,1
%A A352263 _Michel Marcus_, Mar 10 2022