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A080607 Golomb's sequence using multiples of 3. 5


%S 3,3,3,6,6,6,9,9,9,12,12,12,12,12,12,15,15,15,15,15,15,18,18,18,18,18,

%T 18,21,21,21,21,21,21,21,21,21,24,24,24,24,24,24,24,24,24,27,27,27,27,

%U 27,27,27,27,27,30,30,30,30,30,30,30,30,30,30,30,30,33,33,33,33,33,33

%N Golomb's sequence using multiples of 3.

%C More generally let b(k) be a sequence of integers in arithmetic progression: b(k) = A*k+B, then the Golomb's sequence a(n) using b(k) is asymptotic to tau^(2-tau)*(A*n)^(tau-1).

%H Ivan Neretin, <a href="/A080607/b080607.txt">Table of n, a(n) for n = 1..10062</a>

%F a(n) is asymptotic to tau^(2-tau)*(3n)^(tau-1) and more precisely it seems that a(n) = round(tau^(2-tau)*(3n)^(tau-1)) +(-2, -1, +0, +1 or +1) where tau is the golden ratio.

%e Read 3,3,3,6,6,6,9,9,9,12,12,12,12,12,12,15 as (3,3,3),(6,6,6),(9,9,9),(12,12,12,12,12,12),... count occurrences between 2 parentheses, gives 3,3,3,6,... which is the sequence itself.

%t a = {3, 3, 3}; Do[a = Join[a, Array[3i&, a[[i]]]], {i, 2, 11}]; a (* _Ivan Neretin_, Apr 03 2015 *)

%Y Cf. A001462, A080606, A080605.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 25 2003

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Last modified December 7 17:25 EST 2022. Contains 358668 sequences. (Running on oeis4.)