A352265 - OEIS

A352265

Integers that need 7 iterations of the map x->A352172(x) to reach 1.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..47.

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