A352268 Integers that need 10 iterations of the map x->A352172(x) to reach 1.

55, 155, 505, 515, 550, 551, 1055, 1155, 1505, 1515, 1550, 1551, 2555, 5005, 5015, 5050, 5051, 5105, 5115, 5150, 5151, 5255, 5500, 5501, 5510, 5511, 5525, 5552, 10055, 10155, 10505, 10515, 10550, 10551, 11055, 11155, 11505, 11515, 11550, 11551, 12555, 15005, 15015, 15050

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Example

55 -> 15625 -> 27000000 -> 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[15050], q[#, 10] &] (* Amiram Eldar, Mar 10 2022 *)

Prog

(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok10(n) = {for (k=1, 10, n = f(n); if ((n==1), return(k==10)); ); }
(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=10):
    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(15051) if ok(k)]) # Michael S. Branicky, Mar 10 2022

Crossrefs

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352266, A352267.

Sequence in context: A043510 A044387 A044768 * A276050 A256353 A068641

Adjacent sequences: A352265 A352266 A352267 * A352269 A352270 A352271

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved