cp's OEIS Frontend

A352261 Integers that need 3 iterations of the map x->A352172(x) to reach 1.

%I A352261 #13 Mar 10 2022 17:32:47
%S A352261 5,8,15,18,24,42,50,51,80,81,105,108,115,118,124,142,150,151,180,181,
%T A352261 204,214,222,240,241,255,258,285,402,412,420,421,445,454,500,501,510,
%U A352261 511,525,528,544,552,582,800,801,810,811,825,852,1005,1008,1015,1018,1024,1042,1050
%N A352261 Integers that need 3 iterations of the map x->A352172(x) to reach 1.
%e A352261 5 -> 125 -> 1000 -> 1.
%t A352261 f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[1050], q[#, 3] &] (* _Amiram Eldar_, Mar 10 2022 *)
%o A352261 (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
%o A352261 isok3(n) = {for (k=1, 3, n = f(n); if ((n==1), return(k==3)););}
%o A352261 (Python)
%o A352261 from math import prod
%o A352261 def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
%o A352261 def ok(x, iters=3):
%o A352261     i = 0
%o A352261     while i < iters and x != 1: i, x = i+1, A352172(x)
%o A352261     return i == iters and x == 1
%o A352261 print([k for k in range(1051) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022
%Y A352261 Cf. A352172. Subsequence of A351876.
%Y A352261 Cf. A352260, A352262, A352263, A352264, A352265, A352266, A352267, A352268.
%K A352261 nonn,base
%O A352261 1,1
%A A352261 _Michel Marcus_, Mar 10 2022