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A074212
Number of steps to reach an integer starting with (2^n + 1)/2^n and iterating the map x->x*ceiling(x).
0
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
1,2
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
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 *)
CROSSREFS
Cf. A073524.
Sequence in context: A327613 A213954 A357067 * A125715 A129283 A332844
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Sep 17 2002
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
STATUS
approved