A352263 Integers that need 5 iterations of the map x->A352172(x) to reach 1.

679, 697, 769, 796, 967, 976, 1679, 1697, 1769, 1796, 1967, 1976, 2379, 2397, 2739, 2793, 2937, 2973, 3279, 3297, 3367, 3376, 3637, 3673, 3729, 3736, 3763, 3792, 3927, 3972, 6079, 6097, 6179, 6197, 6337, 6373, 6709, 6719, 6733, 6790, 6791, 6907, 6917, 6970, 6971, 7069, 7096

Offset

1,1

Links

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

Example

679 -> 54010152 -> 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[7096], q[#, 5] &] (* Amiram Eldar, Mar 10 2022 *)

Prog

(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok5(n) = {for (k=1, 5, n = f(n); if ((n==1), return(k==5)); ); }
(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=5):
    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(7100) if ok(k)]) # Michael S. Branicky, Mar 10 2022

Crossrefs

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352264, A352265, A352266, A352267, A352268.

Sequence in context: A121105 A046514 A199995 * A340091 A374556 A164650

Adjacent sequences: A352260 A352261 A352262 * A352264 A352265 A352266

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved