This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A048735 a(n) = (n AND floor(n/2)), where AND is bitwise and-operator (A004198). 13
 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 0, 0, 0, 1, 0, 0, 2, 3, 8, 8, 8, 9, 12, 12, 14, 15, 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 16, 16, 16, 17, 16, 16, 18, 19, 24, 24, 24, 25, 28, 28, 30, 31, 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 0 (list; graph; refs; listen; history; text; internal format)
 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). The number of 1's through 4*2^n appears to yield A000045(n+1). - Ben Burns, Jun 12 2017 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 Cf. A003714 (positions of zeros), A003188, A050600. Sequence in context: A037882 A024865 A025109 * A102037 A286530 A152857 Adjacent sequences:  A048732 A048733 A048734 * A048736 A048737 A048738 KEYWORD nonn,base AUTHOR Antti Karttunen, Apr 26 1999 EXTENSIONS New formula and more terms added by Antti Karttunen, Jan 01 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 16:48 EDT 2019. Contains 327242 sequences. (Running on oeis4.)