A087704 Number of steps for iteration of map x -> (5/3)*floor(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.

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

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.

Formula

a(n) = a(n + m) if a(n) > 0 and m is a (positive or negative) multiple of 3^a(n). - Robert Israel, Sep 01 2023

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)[2], n=2..60)];

Prog

(Python)
from fractions import Fraction
def A087704(n):
    x, c = Fraction(n, 1), 0
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x.__floor__(), 3)
        c += 1
    return c # Chai Wah Wu, Sep 01 2023

Crossrefs

Cf. A087705, A087706, A087707.

Sequence in context: A350228 A199087 A306913 * A165092 A306915 A270743

Adjacent sequences: A087701 A087702 A087703 * A087705 A087706 A087707

Keyword

nonn

Author

N. J. A. Sloane, Sep 29 2003

Status

approved