cp's OEIS Frontend

A352266 Integers that need 8 iterations of the map x->A352172(x) to reach 1.

%I A352266 #11 Mar 10 2022 17:33:16
%S A352266 27,57,72,75,127,157,172,175,207,217,270,271,355,457,475,507,517,535,
%T A352266 547,553,570,571,574,702,705,712,715,720,721,745,750,751,754,1027,
%U A352266 1057,1072,1075,1127,1157,1172,1175,1207,1217,1270,1271,1355,1457,1475,1507,1517,1535,1547
%N A352266 Integers that need 8 iterations of the map x->A352172(x) to reach 1.
%e A352266 27 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
%t A352266 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[1547], q[#, 8] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352266 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352266 isok8(n) = {for (k=1, 8, n = f(n); if ((n==1), return(k==8)););}
%o A352266 (Python)
%o A352266 from math import prod
%o A352266 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352266 def ok(x, iters=8):
%o A352266     i = 0
%o A352266     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352266     return i == iters and x == 1
%o A352266 print([k for k in range(1548) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352266 Cf. A352172. Subsequence of A351876.
%Y A352266 Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352267, A352268.
%K A352266 nonn,base
%O A352266 1,1
%A A352266 _Michel Marcus_, Mar 10 2022