OFFSET
1,1
COMMENTS
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).
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10062
FORMULA
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.
EXAMPLE
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.
MATHEMATICA
a = {3, 3, 3}; Do[a = Join[a, Array[3i&, a[[i]]]], {i, 2, 11}]; a (* Ivan Neretin, Apr 03 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 25 2003
STATUS
approved