A087705 First integer > n reached under iteration of map x -> (5/3)*floor(x) when started at n, or -1 if no such integer is ever reached.

5, 5, 10, 35, 10, 30, 35, 15, 905, 30, 20, 35, 105, 25, 905, 210, 30, 85, 55, 35, 60, 105, 40, 2410, 905, 45, 210, 80, 50, 85, 405, 55, 155, 160, 60, 280, 105, 65, 110, 2410, 70, 905, 335, 75, 210, 130, 80, 135, 230, 85, 660, 405, 90, 1160, 155, 95, 160, 2085, 100

Offset

2,1

Comments

It is conjectured that an integer is always reached.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

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

Maple

f2 := proc(x, y) x*floor(y); end; r := 5/3; h := proc(x) local n, y; global r; y := f2(r, x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x, n, y]); else y := f2(r, y); fi; od: RETURN(['NULL', 'NULL', 'NULL']); end; [seq(h(n)[3], n=2..60)];

Prog

(Python)
from fractions import Fraction
def A087705(n):
    x = Fraction(n, 1)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x.__floor__(), 3)
    return int(x) # Chai Wah Wu, Sep 01 2023

Crossrefs

Cf. A087704, A087706.

Sequence in context: A298181 A290332 A302842 * A087033 A175902 A079305

Adjacent sequences: A087702 A087703 A087704 * A087706 A087707 A087708

Keyword

nonn

Author

N. J. A. Sloane, Sep 29 2003

Status

approved