A074212 Number of steps to reach an integer starting with (2^n + 1)/2^n and iterating the map x->x*ceiling(x).

1, 3, 4, 8, 6, 6, 14, 14, 15, 9, 12, 20, 21, 21, 22, 30, 28, 33, 22, 11, 16, 34, 31, 23, 32, 30, 25, 43, 32, 29, 35, 40, 31, 58, 49, 47, 39, 43, 45, 46, 39, 44, 32, 44, 22, 56, 51, 61, 48, 46, 55, 68, 69, 60, 69, 70, 78, 89, 72, 93, 61, 64, 80, 71, 60, 58, 71

Offset: 1

Author

Benoit Cloitre, Sep 17 2002

Keywords

• nonn

Comments

Is a(n) > n for n > 10? Does lim_{n->infinity} a(n)/n exist?

a(n) <= n for n = 1, 6, 10, 20, 21, 24, 27, ... - Amiram Eldar, Nov 28 2020

Crossrefs

Cf. A073524.

Programs

Mathematica

a[n_] := Module[{x = (2^n + 1)/2^n, nstep = 0}, While[!IntegerQ[x], nstep++; x *= Ceiling[x]]; nstep]; Array[a, 15] (* Amiram Eldar, Nov 28 2020 *)

Extensions

a(16)-a(17) from Ryan Propper, Mar 18 2008

a(18)-a(21) from Lars Blomberg, Jan 17 2013

a(22)-a(27) from Amiram Eldar, Nov 28 2020

More terms from Jinyuan Wang, Jan 15 2022