A087707 Number of steps for iteration of map x -> (5/3)*ceiling(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.

5, 4, 1, 3, 2, 1, 2, 3, 1, 10, 4, 1, 6, 2, 1, 2, 9, 1, 3, 3, 1, 5, 2, 1, 2, 5, 1, 4, 8, 1, 3, 2, 1, 2, 3, 1, 4, 12, 1, 5, 2, 1, 2, 4, 1, 3, 3, 1, 7, 2, 1, 2, 4, 1, 5, 6, 1, 3, 2, 1, 2, 3, 1, 11, 5, 1, 4, 2, 1, 2, 6, 1, 3, 3, 1, 4, 2, 1, 2, 5, 1, 6, 4, 1, 3, 2, 1, 2, 3, 1, 6, 4, 1, 5, 2, 1, 2, 5, 1, 3

Offset

1,1

Comments

It is conjectured that an integer is always reached.

Links

Table of n, a(n) for n=1..100.

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

Maple

c2 := proc(x, y) x*ceil(y); end; r := 5/3; ch := proc(x) local n, y; global r; y := c2(r, x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x, n, y]); else y := c2(r, y); fi; od: RETURN(['NULL', 'NULL', 'NULL']); end; [seq(ch(n)[2], n=1..100)];

Prog

(Python)
from fractions import Fraction
def A087707(n):
    x, c = Fraction(n), 0
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x.__ceil__(), 3)
        c += 1
    return c # Chai Wah Wu, Sep 02 2023

Crossrefs

Cf. A087704, A087705, A087706, A087708, A087709.

Sequence in context: A351123 A166044 A190287 * A198352 A113011 A028875

Adjacent sequences: A087704 A087705 A087706 * A087708 A087709 A087710

Keyword

nonn

Author

N. J. A. Sloane, Sep 29 2003

Status

approved