cp's OEIS Frontend

A087665 Consider recurrence b(0) = n/4, b(k) = b(k-1)*floor(b(k-1)); sequence gives first integer reached, or -1 if no integer is ever reached.

%I A087665 #17 Feb 18 2021 16:07:18
%S A087665 2,18,5,550935,3,3396542576998428,105
%N A087665 Consider recurrence b(0) = n/4, b(k) = b(k-1)*floor(b(k-1)); sequence gives first integer reached, or -1 if no integer is ever reached.
%C A087665 It is conjectured that an integer is always reached if the initial value is >= 2.
%C A087665 a(133) has 6227 digits. - _Michael S. Branicky_, Feb 18 2021
%H A087665 Michael S. Branicky, <a href="/A087665/b087665.txt">Table of n, a(n) for n = 8..132</a>
%H A087665 J. C. Lagarias and N. J. A. Sloane, Approximate squaring (<a href="http://neilsloane.com/doc/apsq.pdf">pdf</a>, <a href="http://neilsloane.com/doc/apsq.ps">ps</a>), Experimental Math., 13 (2004), 113-128.
%o A087665 (Python)
%o A087665 from fractions import Fraction
%o A087665 def a(n):
%o A087665   b = Fraction(n, 4)
%o A087665   while b.denominator != 1: b *= int(b)
%o A087665   return b
%o A087665 for n in range(8, 15): print(a(n)) # _Michael S. Branicky_, Feb 18 2021
%Y A087665 Cf. A087664 (steps to reach an integer), A087667, A087668.
%K A087665 nonn
%O A087665 8,1
%A A087665 _N. J. A. Sloane_, Sep 27 2003
%E A087665 The next term is too large to include.