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

Author

Marc LeBrun, Oct 31 2001

Keywords

• base
• easy
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A065362, A030341.

Programs

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

Mathematica

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

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

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