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A080607 Golomb's sequence using multiples of 3. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 16:06 EST 2017. Contains 295905 sequences.