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

Author

Michel Marcus, Mar 10 2022

Keywords

• nonn
• base

Examples

			3 -> 27 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
		

Crossrefs

Cf. A352172. Subsequence of A351876.

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

Programs

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 *)

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