A279645 a(n) = not (n XOR (n shift 1)).

0, 0, 0, 1, 1, 0, 2, 3, 3, 2, 0, 1, 5, 4, 6, 7, 7, 6, 4, 5, 1, 0, 2, 3, 11, 10, 8, 9, 13, 12, 14, 15, 15, 14, 12, 13, 9, 8, 10, 11, 3, 2, 0, 1, 5, 4, 6, 7, 23, 22, 20, 21, 17, 16, 18, 19, 27, 26, 24, 25, 29, 28, 30, 31, 31, 30, 28, 29, 25, 24, 26, 27, 19, 18, 16

Offset: 0

Author

Paolo P. Lava, Dec 16 2016

Keywords

• nonn
• easy
• look

Comments

In other words, a(n) = the binary complement of (n XOR (n shift 1)). - N. J. A. Sloane, Mar 14 2024

Values of n for which a(n) = 0 are given by A000975(k).

Values of n for which a(n) = 1 are given by A097072(k) (for k>1).

Examples

			5044 converted to base 2 is 1001110110100.
Then consider each pair of adjacent bits starting from MSD: if they are equal, 00 or 11, set 1 otherwise 0:
  (1+0) -> 0
  (0+0) -> 1
  (0+1) -> 0
  (1+1) -> 1
  (1+1) -> 1
  (1+0) -> 0
  (0+1) -> 0
  (1+1) -> 1
  (1+0) -> 0
  (0+1) -> 0
  (1+0) -> 0
  (0+0) -> 1
We get 10110010001, so a(5044) = 1425.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..10000
• Paolo P. Lava, First occurrence of n in A279645, for n <= 1000
• Paolo P. Lava, Graph of the first 10000 terms
• Paolo P. Lava, Graph of the first occurrence of n in A279645, for n <= 1000

Crossrefs

Cf. A000975, A038554, A097072.

Programs

Maple

P:=proc(n) local a,b,k; a:=0; b:=convert(n,base,2);
for k to nops(b)-1 do a:=a+((((b[k]+b[k+1]) mod 2)+1) mod 2)*2^(k-1); od; RETURN(a); end;
[seq(P(i),i=0..100)];
# alternative ( R. J. Mathar, Jun 22 2020)
A279645 := proc(n)
    local dgs,L ;
    dgs := convert(n,base,2) ;
    L := [] ;
    for i from 2 to nops(dgs) do
        if op(i,dgs) = op(i-1,dgs) then
            L := [op(L),1] ;
        else
            L := [op(L),0] ;
        fi ;
    end do:
    add( op(i,L)*2^(i-1),i=1..nops(L)) ;
end proc:

Mathematica

a[n_] := Partition[IntegerDigits[n, 2], 2, 1] /. {b_Integer, c_Integer} :> If[b == c, 1, 0] // FromDigits[#, 2]&;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 08 2023 *)