cp's OEIS Frontend

A352267 Integers that need 9 iterations of the map x->A352172(x) to reach 1.

%I A352267 #11 Mar 10 2022 17:33:10
%S A352267 3,13,30,31,56,65,103,113,130,131,156,165,235,253,300,301,310,311,325,
%T A352267 352,506,516,523,532,560,561,605,615,650,651,1003,1013,1030,1031,1056,
%U A352267 1065,1103,1113,1130,1131,1156,1165,1235,1253,1300,1301,1310,1311,1325,1352,1506,1516
%N A352267 Integers that need 9 iterations of the map x->A352172(x) to reach 1.
%e A352267 3 -> 27 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
%t A352267 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[1516], q[#, 9] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352267 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352267 isok9(n) = {for (k=1, 9, n = f(n); if ((n==1), return(k==9)););}
%o A352267 (Python)
%o A352267 from math import prod
%o A352267 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352267 def ok(x, iters=9):
%o A352267     i = 0
%o A352267     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352267     return i == iters and x == 1
%o A352267 print([k for k in range(1517) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352267 Cf. A352172. Subsequence of A351876.
%Y A352267 Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352266, A352268.
%K A352267 nonn,base
%O A352267 1,1
%A A352267 _Michel Marcus_, Mar 10 2022