OFFSET
0,7
COMMENTS
To prove that (n AND floor(n/2)) = (3n-(n XOR 2n))/4 (= A048728(n)/4), we first multiply both sides by 4, to get 2*(n AND 2n) = (3n - (n XOR 2n)) and then rearrange terms: 3n = (n XOR 2n) + 2*(n AND 2n), which fits perfectly to the identity A+B = (A XOR B) + 2*(A AND B) (given by Schroeppel in HAKMEM link).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1023
Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 23 (Schroeppel)
FORMULA
a(n) = A048728(n)/4. (This was the original definition. AND-formula found Jan 01 2007).
MAPLE
seq(Bits:-And(n, floor(n/2)), n=0..200); # Robert Israel, Feb 29 2016
MATHEMATICA
Table[BitAnd[n, Floor[n/2]], {n, 0, 127}] (* T. D. Noe, Aug 13 2012 *)
PROG
(PARI) a(n) = bitand(n, n\2); \\ Michel Marcus, Feb 29 2016
(Python)
def a(n): return n&int(n/2) # Indranil Ghosh, Jun 13 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Apr 26 1999
EXTENSIONS
New formula and more terms added by Antti Karttunen, Jan 01 2007
STATUS
approved