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

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

Cf. A352172. Subsequence of A351876.

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

Sequence in context: A277964 A043497 A051804 * A121022 A277589 A069164

Adjacent sequences: A352259 A352260 A352261 * A352263 A352264 A352265

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved