A352267 Integers that need 9 iterations of the map x->A352172(x) to reach 1.

3, 13, 30, 31, 56, 65, 103, 113, 130, 131, 156, 165, 235, 253, 300, 301, 310, 311, 325, 352, 506, 516, 523, 532, 560, 561, 605, 615, 650, 651, 1003, 1013, 1030, 1031, 1056, 1065, 1103, 1113, 1130, 1131, 1156, 1165, 1235, 1253, 1300, 1301, 1310, 1311, 1325, 1352, 1506, 1516

Offset

1,1

Links

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

Example

3 -> 27 -> 2744 -> 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[1516], q[#, 9] &] (* Amiram Eldar, Mar 10 2022 *)

Prog

(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok9(n) = {for (k=1, 9, n = f(n); if ((n==1), return(k==9)); ); }
(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=9):
    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(1517) if ok(k)]) # Michael S. Branicky, Mar 10 2022

Crossrefs

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352266, A352268.

Sequence in context: A183436 A154300 A051805 * A330451 A022264 A288541

Adjacent sequences: A352264 A352265 A352266 * A352268 A352269 A352270

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved