cp's OEIS Frontend

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

%I A326735 #13 Feb 21 2021 06:29:00
%S A326735 2,21,28,36,44,62,93,102,112,122,132,142,152,162,172,182,192,202,211,
%T A326735 227,229,247,256,258,263,264,272,281,286,293,302,317,324,336,342,344,
%U A326735 349,353,358,361,376,382,402,417,419,427,433,434,441,446,456,497,502,552
%N A326735 Numbers which converge to 2 under repeated application of the powertrain map of A133500.
%e A326735 28 -> 2^8 = 256 -> 2^5*6 = 192 -> 1^9*2 = 2.
%o A326735 (Python) # change target for A326733-A326742, A135384, A309385
%o A326735 def powertrain(n):
%o A326735   p, s = 1, str(n)
%o A326735   if len(s)%2 == 1: s += '1'
%o A326735   for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
%o A326735   return p
%o A326735 def aupto(limit, target=0):
%o A326735   alst = []
%o A326735   for n in range(1, limit+1):
%o A326735     m, ptm = n, powertrain(n)
%o A326735     while m != ptm: m, ptm = ptm, powertrain(ptm)
%o A326735     if m == target: alst.append(n)
%o A326735   return alst
%o A326735 print(aupto(552, target=2)) # _Michael S. Branicky_, Feb 21 2021
%Y A326735 Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326736, A326737, A326738, A326739, A326740, A326741, A326742.
%K A326735 nonn,base,easy
%O A326735 1,1
%A A326735 _Martin Renner_, Jul 22 2019