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A065361
Rebase n from 3 to 2. Replace 3^k with 2^k in ternary expansion of n.
19
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
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
Sequence in context: A245433 A168560 A333942 * A089792 A081608 A096532
KEYWORD
base,easy,nonn
AUTHOR
Marc LeBrun, Oct 31 2001
STATUS
approved