A080606 Golomb's sequence using even integers.

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, 14, 14, 14, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 22, 22, 22, 22, 22, 22, 22, 22, 24, 24, 24, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26

Offset: 1

Author

Benoit Cloitre, Feb 25 2003

Keywords

• nonn

Examples

			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.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001462, A080605, A080607.

Programs

Mathematica

a = {2, 2}; Do[a = Join[a, Array[2i&, a[[i]]]], {i, 2, 13}]; a (* Ivan Neretin, Apr 03 2015 *)

Formula

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.