A352262 - OEIS

%I #13 Mar 10 2022 17:32:52

%S 2,12,20,21,45,54,102,112,120,121,145,154,200,201,210,211,225,252,405,

%T 415,450,451,504,514,522,540,541,558,585,855,1002,1012,1020,1021,1045,

%U 1054,1102,1112,1120,1121,1145,1154,1200,1201,1210,1211,1225,1252,1405,1415,1450,1451

%N Integers that need 4 iterations of the map x->A352172(x) to reach 1.

%e 2 -> 8 -> 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[1451], q[#, 4] &] (* _Amiram Eldar_, Mar 10 2022 *)

%o (PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172

%o isok4(n) = {for (k=1, 4, n = f(n); if ((n==1), return(k==4)););}

%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=4):

%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(1452) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022

%Y Cf. A352172. Subsequence of A351876.

%Y Cf. A352260, A352261, A352263, A352264, A352265, A352266, A352267, A352268.

%K nonn,base

%O 1,1

%A _Michel Marcus_, Mar 10 2022