A087708 First integer > n reached under iteration of map x -> (5/3)*ceiling(x) when started at n, or -1 if no such integer is ever reached.

20, 20, 5, 20, 15, 10, 20, 40, 15, 1770, 90, 20, 290, 40, 25, 45, 1770, 30, 90, 95, 35, 290, 65, 40, 70, 345, 45, 220, 1770, 50, 145, 90, 55, 95, 165, 60, 290, 17845, 65, 520, 115, 70, 120, 345, 75, 215, 220, 80, 1770, 140, 85, 145, 415, 90, 715, 1215, 95, 270, 165, 100, 170

Offset

1,1

Comments

It is conjectured that an integer is always reached.

Links

Table of n, a(n) for n=1..61.

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)[3], n=1..100)];

Prog

(Python)
from fractions import Fraction
def A087708(n):
    x = Fraction(n)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x.__ceil__(), 3)
    return int(x) # Chai Wah Wu, Sep 02 2023

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087709.

Sequence in context: A172164 A267058 A205545 * A220022 A217517 A332561

Adjacent sequences: A087705 A087706 A087707 * A087709 A087710 A087711

Keyword

nonn

Author

N. J. A. Sloane, Sep 29 2003

Status

approved