A352266 Integers that need 8 iterations of the map x->A352172(x) to reach 1.

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

Links

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

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

Cf. A352172. Subsequence of A351876.

Cf. A352260, A352261, A352262, A352263, A352264, A352265, A352267, A352268.

Sequence in context: A042454 A042456 A132768 * A053180 A080864 A260440

Adjacent sequences: A352263 A352264 A352265 * A352267 A352268 A352269

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2022

Status

approved