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Golomb's sequence using even integers.
7

%I #12 Apr 04 2015 02:40:28

%S 2,2,4,4,6,6,6,6,8,8,8,8,10,10,10,10,10,10,12,12,12,12,12,12,14,14,14,

%T 14,14,14,16,16,16,16,16,16,18,18,18,18,18,18,18,18,20,20,20,20,20,20,

%U 20,20,22,22,22,22,22,22,22,22,24,24,24,24,24,24,24,24,26,26,26,26,26

%N Golomb's sequence using even integers.

%H Ivan Neretin, <a href="/A080606/b080606.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) is asymptotic to tau^(2-tau)*(2n)^(tau-1) and more precisely it seems that a(n) = round(tau^(2-tau)*(2n)^(tau-1)) +(-1, +0 or +1) where tau is the golden ratio.

%e Read 2,2,4,4,6,6,6,6,8,8,8,8,10,10,10,10,10,10 as (2,2),(4,4),(6,6,6,6),(8,8,8,8),(10,10,10,10,10,10) count occurrences between 2 parentheses, gives 2,2,4,4,6,... which is the sequence itself.

%t a = {2, 2}; Do[a = Join[a, Array[2i&, a[[i]]]], {i, 2, 13}]; a (* _Ivan Neretin_, Apr 03 2015 *)

%Y Cf. A001462, A080605, A080607.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 25 2003