A163325 Pick digits at the even distance from the least significant end of the ternary expansion of n, then convert back to decimal.

0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 7, 8, 6, 7, 8, 6, 7, 8, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 7, 8, 6, 7, 8, 6, 7, 8, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 7, 8, 6, 7, 8, 6, 7, 8, 9, 10, 11, 9, 10, 11, 9, 10, 11, 12, 13, 14, 12, 13, 14

Offset: 0

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• base
• look

Examples

			11 in ternary base (A007089) is written as '102' (1*9 + 0*3 + 2), from which we pick the "zeroth" and 2nd digits from the right, giving '12' = 1*3 + 2 = 5, thus a(11) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..728
• Kevin Ryde, Plot2 of X=A163325,Y=A163326, illustrating the ternary Z-order curve.
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

A059905 is an analogous sequence for binary.

Cf. A007089, A163327, A163328, A163329.

Programs

PARI

a(n) = fromdigits(digits(n,9)%3,3); \\ Kevin Ryde, May 14 2020

Formula

a(0) = 0, a(n) = (n mod 3) + 3*a(floor(n/9)).

a(n) = Sum_{k>=0} {A030341(n,k)*b(k)} where b is the sequence (1,0,3,0,9,0,27,0,81,0,243,0... = A254006): powers of 3 alternating with zeros. - Philippe Deléham, Oct 22 2011

A037314(a(n)) + 3*A037314(A163326(n)) = n for all n.

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009