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.

2, 18, 5, 550935, 3, 3396542576998428, 105

Offset: 8

Author

N. J. A. Sloane, Sep 27 2003

Keywords

• nonn

Comments

It is conjectured that an integer is always reached if the initial value is >= 2.

a(133) has 6227 digits. - Michael S. Branicky, Feb 18 2021

Links

• Michael S. Branicky, Table of n, a(n) for n = 8..132
• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

Cf. A087664 (steps to reach an integer), A087667, A087668.

Programs

Python

from fractions import Fraction
def a(n):
  b = Fraction(n, 4)
  while b.denominator != 1: b *= int(b)
  return b
for n in range(8, 15): print(a(n)) # Michael S. Branicky, Feb 18 2021

Extensions

The next term is too large to include.