A087668 -id:A087668 - cp's OEIS frontend

A087664 Consider recurrence b(0) = n/4, b(k) = b(k-1)*floor(b(k-1)); sequence gives number of steps to reach an integer, or -1 if no integer is ever reached.

0, 2, 1, 4, 0, 5, 2, 9, 0, 1, 1, 1, 0, 3, 3, 2, 0, 4, 1, 2, 0, 6, 2, 7, 0, 1, 1, 1, 0, 5, 4, 4, 0, 2, 1, 3, 0, 8, 2, 7, 0, 1, 1, 1, 0, 2, 3, 6, 0, 3, 1, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 4, 5, 5, 0, 2, 1, 6, 0, 5, 2, 4, 0, 1, 1, 1, 0, 4, 3, 2, 0, 5, 1, 2, 0, 3, 2, 3, 0, 1, 1, 1, 0, 4, 4, 6, 0, 2, 1, 3, 0, 3, 2, 3, 0

Offset: 8

N. J. A. Sloane, Sep 27 2003

nonn

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

J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Cf. A087665 (integer reached), A087667 and A087668 (records), A057016.

More terms from John W. Layman, Sep 27 2003

A087667 Records in A087664.

Original entry on oeis.org

0, 2, 4, 5, 9, 12, 16, 24, 29, 30, 31, 32, 36, 37, 42

Offset: 1

N. J. A. Sloane, Sep 27 2003

Cf. A087664, A087668.

A087664(n)={ local(x,s) ; x=n/4 ; s=0 ; while( type(x)!="t_INT", x *= floor(x) ; s++ ; ) ; return(s) ; } { rec=-1 ; for(n=8,1000000, a=A087664(n) ; if(a>rec, rec=a ; print(rec) ; ) ; ) ; } - R. J. Mathar, Nov 25 2006

a(n)=A087664(A087668(n)). - R. J. Mathar, Nov 25 2006

More terms from R. J. Mathar, Nov 25 2006

a(8)-a(15) from Max Alekseyev, Jul 30 2011

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.

Original entry on oeis.org

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

Offset: 8

N. J. A. Sloane, Sep 27 2003

nonn

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

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.

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

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

The next term is too large to include.

cp's OEIS Frontend

A087664 Consider recurrence b(0) = n/4, b(k) = b(k-1)*floor(b(k-1)); sequence gives number of steps to reach an integer, or -1 if no integer is ever reached.

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A087667 Records in A087664.

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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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Python

Extensions