A072340 Number of steps to reach an integer starting with n/3 and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

0, 2, 6, 0, 1, 1, 0, 5, 2, 0, 3, 2, 0, 1, 1, 0, 2, 4, 0, 3, 4, 0, 1, 1, 0, 22, 7, 0, 2, 5, 0, 1, 1, 0, 7, 2, 0, 4, 2, 0, 1, 1, 0, 2, 5, 0, 13, 9, 0, 1, 1, 0, 3, 3, 0, 2, 3, 0, 1, 1, 0, 3, 2, 0, 5, 2, 0, 1, 1, 0, 2, 3, 0, 8, 3, 0, 1, 1, 0, 5, 4, 0, 2, 4, 0, 1, 1, 0, 14, 2, 0, 3, 2, 0, 1, 1, 0, 2, 9, 0, 3, 9, 0, 1, 1

Offset

3,2

Comments

We conjecture that an integer is always reached.

The occurrence of the first 1, 2, 3, 4 etc. is at the indices 7, 4, 13, 20, 10, 5, 29, 76, 50, 452, 244, 830, 49, 91, 319, 2639, 5753, 2215, 6151, 8653, 280, 28, 1783, ... - R. J. Mathar, Nov 25 2006

References

N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.

Links

R. J. Mathar, Table of n, a(n) for n = 3..7147

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

N. J. A. Sloane, Seven Staggering Sequences.

Maple

g := proc(x) local M, t1, t2, t3; M := 3^100; t1 := ceil(x) mod M; t2 := x*t1; t3 := numer(t2) mod M; t3/denom(t2); end;
f := proc(n) local t1, c; global g; if type(n, 'integer') then RETURN(0); fi; t1 := g(n); c := 1; while not type(t1, 'integer') do c := c+1; t1 := g(t1); od; RETURN(c); end;
[seq(f(n/3), n=3..120)]; # this gives the correct answer as long as the answer is < 99.

Mathematica

a[n_] := Module[{x = n/3, s = 0}, While[!IntegerQ[x], x *= Ceiling[x]; s++]; s]; Table[a[n], {n, 3, 107}] (* Jean-François Alcover, Jan 27 2019, from PARI *)

Prog

(PARI) A072340(n)={ local(x, s); x=n/3; s=0; while( type(x)!="t_INT", x *= ceil(x); s++ ); return(s); } \\ R. J. Mathar, Nov 25 2006

Crossrefs

Cf. A073524, A085276, A085285, A085286.

Sequence in context: A165733 A330327 A039907 * A384946 A118354 A384621

Adjacent sequences: A072337 A072338 A072339 * A072341 A072342 A072343

Keyword

nonn

Author

N. J. A. Sloane and J. C. Lagarias, Sep 03 2002

Status

approved