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

0,3

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

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.

Example

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.

Prog

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

Crossrefs

A059905 is an analogous sequence for binary.

Cf. A007089, A163327, A163328, A163329.

Sequence in context: A055087 A025685 A194515 * A105186 A328346 A238406

Adjacent sequences: A163322 A163323 A163324 * A163326 A163327 A163328

Keyword

nonn,base,look

Author

Antti Karttunen, Jul 29 2009

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009

Status

approved