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

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

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352263, A352264, A352266, A352267, A352268.

Sequence in context: A224453 A227706 A261816 * A020375 A031788 A252543

Adjacent sequences: A352262 A352263 A352264 * A352266 A352267 A352268

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved