A352264 Integers that need 6 iterations of the map x->A352172(x) to reach 1.

377, 737, 773, 1377, 1737, 1773, 3077, 3177, 3707, 3717, 3770, 3771, 3889, 3898, 3988, 4689, 4698, 4869, 4896, 4968, 4986, 5677, 5767, 5776, 6489, 6498, 6577, 6668, 6686, 6757, 6775, 6849, 6866, 6894, 6948, 6984, 7037, 7073, 7137, 7173, 7307, 7317, 7370, 7371, 7567, 7576

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

377 -> 3176523 -> 54010152000 -> 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[7576], q[#, 6] &] (* Amiram Eldar, Mar 10 2022 *)

Prog

(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok6(n) = {for (k=1, 6, n = f(n); if ((n==1), return(k==6)); ); }
(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=6):
    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(7577) if ok(k)]) # Michael S. Branicky, Mar 10 2022

Crossrefs

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352263, A352265, A352266, A352267, A352268.

Sequence in context: A198640 A171489 A105717 * A222350 A277942 A241908

Adjacent sequences: A352261 A352262 A352263 * A352265 A352266 A352267

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved