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.

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

Author

Clark Kimberling, Jun 11 2006

Keywords

• nonn

Comments

Self-inverse permutation of the natural numbers.

Examples

			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.
		

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).

Links

• Seqfan: about Murthy's sequence A073675 (1)
• Seqfan: about Murthy's sequence A073675 (2)
• Seqfan: about Murthy's sequence A073675 (3)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A073675, A120230.

Row 3 and column 3 of A059897.

Formula

a(n) = [n/3] if this is positive and new, otherwise a(n)=3n.