A087707 - OEIS

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

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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