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A352266
Integers that need 8 iterations of the map x->A352172(x) to reach 1.
8
27, 57, 72, 75, 127, 157, 172, 175, 207, 217, 270, 271, 355, 457, 475, 507, 517, 535, 547, 553, 570, 571, 574, 702, 705, 712, 715, 720, 721, 745, 750, 751, 754, 1027, 1057, 1072, 1075, 1127, 1157, 1172, 1175, 1207, 1217, 1270, 1271, 1355, 1457, 1475, 1507, 1517, 1535, 1547
OFFSET
1,1
EXAMPLE
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[1547], q[#, 8] &] (* Amiram Eldar, Mar 10 2022 *)
PROG
(PARI) f(n) = vecprod(apply(x->x^3, select(x->(x>1), digits(n)))); \\ A352172
isok8(n) = {for (k=1, 8, n = f(n); if ((n==1), return(k==8)); ); }
(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=8):
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(1548) if ok(k)]) # Michael S. Branicky, Mar 10 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 10 2022
STATUS
approved