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A326742
Numbers which converge to 9 under repeated application of the powertrain map of A133500.
10
9, 25, 32, 52, 91, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 228, 234, 242, 251, 279, 295, 309, 313, 321, 337, 377, 409, 418, 422, 509, 515, 521, 539, 544, 609, 709, 809, 814, 835, 909, 911, 965, 1025, 1032, 1052, 1091, 1125, 1132, 1152, 1191
OFFSET
1,1
EXAMPLE
25 -> 2^5 = 32 -> 3^2 = 9.
PROG
(Python)
def powertrain(n):
p, s = 1, str(n)
if len(s)%2 == 1: s += '1'
for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
return p
def aupto(limit, target=0):
alst = []
for n in range(1, limit+1):
m, ptm = n, powertrain(n)
while m != ptm: m, ptm = ptm, powertrain(ptm)
if m == target: alst.append(n)
return alst
print(aupto(1191, target=9)) # Michael S. Branicky, Sep 25 2021
KEYWORD
nonn,base,easy
AUTHOR
Martin Renner, Jul 22 2019
STATUS
approved