A326735 Numbers which converge to 2 under repeated application of the powertrain map of A133500.

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

Author

Martin Renner, Jul 22 2019

Keywords

• nonn
• base
• easy

Examples

			28 -> 2^8 = 256 -> 2^5*6 = 192 -> 1^9*2 = 2.
		

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326736, A326737, A326738, A326739, A326740, A326741, A326742.

Programs

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