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%I #11 Mar 10 2022 17:33:26
%S 377,737,773,1377,1737,1773,3077,3177,3707,3717,3770,3771,3889,3898,
%T 3988,4689,4698,4869,4896,4968,4986,5677,5767,5776,6489,6498,6577,
%U 6668,6686,6757,6775,6849,6866,6894,6948,6984,7037,7073,7137,7173,7307,7317,7370,7371,7567,7576
%N Integers that need 6 iterations of the map x->A352172(x) to reach 1.
%e 377 -> 3176523 -> 54010152000 -> 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[7576], q[#, 6] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o isok6(n) = {for (k=1, 6, n = f(n); if ((n==1), return(k==6)););}
%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=6):
%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(7577) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y Cf. A352172. Subsequence of A351876.
%Y Cf. A352260, A352261, A352262, A352263, A352265, A352266, A352267, A352268.
%K nonn,base
%O 1,1
%A _Michel Marcus_, Mar 10 2022
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