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

1,1

Links

Table of n, a(n) for n=1..54.

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

Crossrefs

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

Sequence in context: A079907 A342727 A075715 * A294377 A071761 A101316

Adjacent sequences: A326732 A326733 A326734 * A326736 A326737 A326738

Keyword

nonn,base,easy

Author

Martin Renner, Jul 22 2019

Status

approved