A352260 Integers that need 2 iterations of the map x->A352172(x) to reach 1.

25, 52, 125, 152, 205, 215, 250, 251, 455, 502, 512, 520, 521, 545, 554, 1025, 1052, 1125, 1152, 1205, 1215, 1250, 1251, 1455, 1502, 1512, 1520, 1521, 1545, 1554, 2005, 2015, 2050, 2051, 2105, 2115, 2150, 2151, 2255, 2500, 2501, 2510, 2511, 2525, 2552, 4055, 4155, 4505

Offset: 1

Author

Michel Marcus, Mar 10 2022

Keywords

• nonn
• base

Examples

			25 -> 1000 -> 1.
		

Crossrefs

Cf. A352172. Subsequence of A351876.

Cf. A352261, A352262, A352263, A352264, A352265, A352266, A352267, 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[4505], q[#, 2] &] (* Amiram Eldar, Mar 10 2022 *)

PARI

f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok2(n) = {for (k=1, 2, n = f(n); if ((n==1), return(k==2)););}

Python

from math import prod
def A352172(n): return prod(int(d)**3 for d in str(n) if d != '0')
def ok(x):
    x = A352172(x)
    return x != 1 and A352172(x) == 1
print([k for k in range(4506) if ok(k)]) # Michael S. Branicky, Mar 10 2022