A087669 The smallest index m such that b(m) is an integer, where b(0)=(2n+1)/n and b(k+1)=b(k)*floor(b(k)) for k>=0.

0, 1, 3, 2, 5, 4, 5, 2, 4, 9, 19, 7, 16, 7, 8, 3, 27, 9, 5, 25, 10, 11, 32, 4, 13, 4, 17, 6, 17, 6, 78, 3, 23, 47, 13, 6, 4, 6, 27, 9, 20, 6, 4, 17, 9, 28, 106, 4, 24, 28, 37, 20, 27, 10, 12, 13, 7, 83, 108, 10, 16, 9, 6, 3, 10, 11, 15, 8, 11, 6, 156, 15, 38, 46, 7

Offset

1,3

Comments

It is conjectured that an integer is always reached if the initial value is >= 2.

Links

Max Alekseyev, Table of n, a(n) for n = 1..10000

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

Maple

A087669 := proc(n) local b, stps ; stps := 0 ; b := (2*n+1)/n ; while not type(b, 'integer') do b := b*floor(b) ; stps := stps+1 ; od ; RETURN(stps) ; end: for n from 1 to 100 do print(n, A087669(n)) ; od ; # R. J. Mathar, Feb 12 2007

Prog

(Python)
def A087669(n):
    c, x = 0, 2*n+1
    a, b = divmod(x, n)
    while b != 0:
        x *= a
        c += 1
        a, b = divmod(x, n)
    return c # Chai Wah Wu, Mar 01 2021

Crossrefs

The records and their indices are given by A192230 and A192229.

Cf. A087670 (integer reached), A087666.

Sequence in context: A292776 A061313 A259846 * A053087 A316519 A062327

Adjacent sequences: A087666 A087667 A087668 * A087670 A087671 A087672

Keyword

nonn

Author

N. J. A. Sloane, Sep 27 2003

Extensions

More terms from R. J. Mathar, Feb 12 2007

Terms a(23) onward from Max Alekseyev, Jun 25 2011

Status

approved