A352262 - OEIS

A352262

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

2, 12, 20, 21, 45, 54, 102, 112, 120, 121, 145, 154, 200, 201, 210, 211, 225, 252, 405, 415, 450, 451, 504, 514, 522, 540, 541, 558, 585, 855, 1002, 1012, 1020, 1021, 1045, 1054, 1102, 1112, 1120, 1121, 1145, 1154, 1200, 1201, 1210, 1211, 1225, 1252, 1405, 1415, 1450, 1451

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

2 -> 8 -> 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[1451], q[#, 4] &] (* Amiram Eldar, Mar 10 2022 *)

PROG

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

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

(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=4):

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(1452) if ok(k)]) # Michael S. Branicky, Mar 10 2022

CROSSREFS