login
A352265
Integers that need 7 iterations of the map x->A352172(x) to reach 1.
8
478, 487, 748, 784, 847, 874, 1478, 1487, 1748, 1784, 1847, 1874, 2278, 2287, 2447, 2474, 2728, 2744, 2782, 2827, 2872, 4078, 4087, 4178, 4187, 4247, 4274, 4427, 4472, 4708, 4718, 4724, 4742, 4780, 4781, 4807, 4817, 4870, 4871, 5788, 5878, 5887, 7048, 7084, 7148, 7184, 7228
OFFSET
1,1
EXAMPLE
478 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
MATHEMATICA
f[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^3; q[n_, len_] := (v = Nest[f, n, len - 1]) != 1 && f[v] == 1; Select[Range[7228], q[#, 7] &] (* Amiram Eldar, Mar 10 2022 *)
PROG
(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok7(n) = {for (k=1, 7, n = f(n); if ((n==1), return(k==7)); ); }
(Python)
from math import prod
def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
def ok(x, iters=7):
i = 0
while i < iters and x != 1: i, x = i+1, A352172(x)
return i == iters and x == 1
print([k for k in range(7229) if ok(k)]) # Michael S. Branicky, Mar 10 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 10 2022
STATUS
approved