login
A120229
Split-floor-multiplier sequence (SFMS) using multipliers 1/3 and 3. The SFMS using multipliers r and s is here introduced: for every positive integer n and positive real number r, let [rn] abbreviate floor(rn). Then SFMS(r, s), where max {r, s} > 1, is the sequence a defined by a(n)=[rn] if [rn] > 0 and is not already in a and a(n) = [sn] otherwise.
13
3, 6, 1, 12, 15, 2, 21, 24, 27, 30, 33, 4, 39, 42, 5, 48, 51, 54, 57, 60, 7, 66, 69, 8, 75, 78, 9, 84, 87, 10, 93, 96, 11, 102, 105, 108, 111, 114, 13, 120, 123, 14, 129, 132, 135, 138, 141, 16, 147, 150, 17, 156, 159, 18, 165, 168, 19, 174, 177, 20, 183, 186, 189, 192, 195
OFFSET
1,1
COMMENTS
Self-inverse permutation of the natural numbers.
REFERENCES
Responses to message "Murthy's sequence A073675" to the seqfan mailing list. The message and responses are dated Feb 02 2006 and relate to generalizations and properties of sequence A073675, which is SFMS(1/2,2).
FORMULA
a(n) = [n/3] if this is positive and new, otherwise a(n)=3n.
EXAMPLE
a(1) = 1*3 because [1/3] is not positive.
a(2) = 2*3 because [2/3] is not positive.
a(3) = 1 = [3*(1/3)].
a(4) = 4*3 because [4/3] = a(3), not new.
CROSSREFS
Row 3 and column 3 of A059897.
Sequence in context: A210033 A209144 A130724 * A266151 A192100 A123534
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 11 2006
STATUS
approved