A326742 - OEIS

%I #10 Sep 25 2021 02:16:21

%S 9,25,32,52,91,109,119,129,139,149,159,169,179,189,199,209,228,234,

%T 242,251,279,295,309,313,321,337,377,409,418,422,509,515,521,539,544,

%U 609,709,809,814,835,909,911,965,1025,1032,1052,1091,1125,1132,1152,1191

%N Numbers which converge to 9 under repeated application of the powertrain map of A133500.

%e 25 -> 2^5 = 32 -> 3^2 = 9.

%o (Python)

%o def powertrain(n):

%o     p, s = 1, str(n)

%o     if len(s)%2 == 1: s += '1'

%o     for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)

%o     return p

%o def aupto(limit, target=0):

%o     alst = []

%o     for n in range(1, limit+1):

%o         m, ptm = n, powertrain(n)

%o         while m != ptm: m, ptm = ptm, powertrain(ptm)

%o         if m == target: alst.append(n)

%o     return alst

%o print(aupto(1191, target=9)) # _Michael S. Branicky_, Sep 25 2021

%Y Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326737, A326738, A326739, A326740, A326741.

%K nonn,base,easy

%O 1,1

%A _Martin Renner_, Jul 22 2019