A065361 Rebase n from 3 to 2. Replace 3^k with 2^k in ternary expansion of n.

0, 1, 2, 2, 3, 4, 4, 5, 6, 4, 5, 6, 6, 7, 8, 8, 9, 10, 8, 9, 10, 10, 11, 12, 12, 13, 14, 8, 9, 10, 10, 11, 12, 12, 13, 14, 12, 13, 14, 14, 15, 16, 16, 17, 18, 16, 17, 18, 18, 19, 20, 20, 21, 22, 16, 17, 18, 18, 19, 20, 20, 21, 22, 20, 21, 22, 22, 23, 24, 24, 25, 26, 24, 25, 26, 26, 27

Offset

0,3

Comments

Notation: (3)[n](2).

Fixed point of the morphism 0->0,1,2; 1->2,3,4; 2->4,5,6; ...; n->2n,2n+1,2n+2. - Philippe Deléham, Oct 22 2011

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Formula

a(0)=0, a(3n)=2*a(n), a(3n+1)=2*a(n)+1, a(3n+2)=2*a(n)+2. - Benoit Cloitre, Dec 21 2002

a(n) = 2*a(floor(n/3))+n-3*floor(n/3). - Benoit Cloitre, Apr 27 2003

a(n) = Sum_{k>=0} A030341(n,k)*2^k. - Philippe Deléham, Oct 22 2011

Example

15 = 120 -> 1(4)+2(2)+0(1) = 8 = a(15).

Mathematica

t = Table[FromDigits[RealDigits[n, 3], 2], {n, 0, 100}]
(* Clark Kimberling, Aug 02 2012 *)

Prog

(PARI) a(n)=if(n<1, 0, if(n%3, a(n-1)+1, 2*a(n/3)))
(PARI) a(n)=if(n<1, 0, 2*a(floor(n/3))+n-3*floor(n/3))
(PARI) Rebase(x, b, c)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=c); return(e) } { for (n=0, 1000, write("b065361.txt", n, " ", Rebase(n, 3, 2)) ) } \\ Harry J. Smith, Oct 17 2009
(Julia)
function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 2
    end
r end; [a(n) for n in 0:76] |> println # Peter Luschny, Jan 03 2021

Crossrefs

Cf. A065362, A030341.

Sequence in context: A245433 A168560 A333942 * A089792 A081608 A096532

Adjacent sequences: A065358 A065359 A065360 * A065362 A065363 A065364

Keyword

base,easy,nonn

Author

Marc LeBrun, Oct 31 2001

Status

approved