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A326735
Numbers which converge to 2 under repeated application of the powertrain map of A133500.
11
2, 21, 28, 36, 44, 62, 93, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 211, 227, 229, 247, 256, 258, 263, 264, 272, 281, 286, 293, 302, 317, 324, 336, 342, 344, 349, 353, 358, 361, 376, 382, 402, 417, 419, 427, 433, 434, 441, 446, 456, 497, 502, 552
OFFSET
1,1
EXAMPLE
28 -> 2^8 = 256 -> 2^5*6 = 192 -> 1^9*2 = 2.
PROG
(Python) # change target for A326733-A326742, A135384, A309385
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(552, target=2)) # Michael S. Branicky, Feb 21 2021
KEYWORD
nonn,base,easy
AUTHOR
Martin Renner, Jul 22 2019
STATUS
approved