OFFSET
0,3
COMMENTS
A032925 is the intersection of this sequence and A023705; cf. A179888. - Reinhard Zumkeller, Jul 31 2010
Fixed point of the morphism: 0-> 0,1,2; 1-> 4,5,6; 2-> 8,9,10; ...; n-> 4n,4n+1,4n+2. - Philippe Deléham, Oct 22 2011
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{i=0..m} d(i)*4^i, where Sum_{i=0..m} d(i)*3^i is the base-3 representation of n. - Clark Kimberling
a(3n) = 4*a(n); a(3n+1) = 4*a(n)+1; a(3n+2) = 4*a(n)+2; a(n) = 4*a(floor(n/3)) + n - 3*floor(n/3). - Benoit Cloitre, Apr 27 2003
a(n) = Sum_{k>=0} A030341(n,k)*4^k. - Philippe Deléham, Oct 22 2011
MATHEMATICA
Select[ Range[ 0, 140 ], (Count[ IntegerDigits[ #, 4 ], 3 ]==0)& ]
PROG
(PARI) a(n)=if(n<1, 0, if(n%3, a(n-1)+1, 4*a(n/3))) or a(n)=if(n<1, 0, 4*a(floor(n/3))+n-3*floor(n/3))
(Haskell)
a023717 n = a023717_list !! (n-1)
a023717_list = filter f [0..] where
f x = x < 3 || (q < 3 && f x') where (x', q) = divMod x 4
-- Reinhard Zumkeller, Apr 18 2015
(Julia)
function a(n)
m, r, b = n, 0, 1
while m > 0
m, q = divrem(m, 3)
r += b * q
b *= 4
end
r end; [a(n) for n in 0:58] |> println # Peter Luschny, Jan 03 2021
(C)
uint32_t a_next(uint32_t a_n) {
uint32_t t = ((a_n ^ 0xaaaaaaaa) | 0x55555555) >> 1;
return (a_n - t) & t;
} // Falk Hüffner, Jan 22 2022
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved