A080607 Golomb's sequence using multiples of 3.

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, 18, 21, 21, 21, 21, 21, 21, 21, 21, 21, 24, 24, 24, 24, 24, 24, 24, 24, 24, 27, 27, 27, 27, 27, 27, 27, 27, 27, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 33, 33, 33, 33, 33, 33

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

Cf. A001462, A080606, A080605.

Sequence in context: A171601 A057944 A281258 * A013322 A211534 A219816

Adjacent sequences: A080604 A080605 A080606 * A080608 A080609 A080610

Keyword

nonn

Author

Benoit Cloitre, Feb 25 2003

Status

approved