A352263 - OEIS

%I #11 Mar 10 2022 17:33:32

%S 679,697,769,796,967,976,1679,1697,1769,1796,1967,1976,2379,2397,2739,

%T 2793,2937,2973,3279,3297,3367,3376,3637,3673,3729,3736,3763,3792,

%U 3927,3972,6079,6097,6179,6197,6337,6373,6709,6719,6733,6790,6791,6907,6917,6970,6971,7069,7096

%N Integers that need 5 iterations of the map x->A352172(x) to reach 1.

%e 679 -> 54010152 -> 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[7096], q[#, 5] &] (* _Amiram Eldar_, Mar 10 2022 *)

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

%o isok5(n) = {for (k=1, 5, n = f(n); if ((n==1), return(k==5)););}

%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=5):

%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(7100) if ok(k)]) # _Michael S. Branicky_, Mar 10 2022

%Y Cf. A352172. Subsequence of A351876.

%Y Cf. A352260, A352261, A352262, A352264, A352265, A352266, A352267, A352268.

%K nonn,base

%O 1,1

%A _Michel Marcus_, Mar 10 2022