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

0,7

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).

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

Example

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.

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 *)

Crossrefs

Cf. A000975, A038554, A097072.

Sequence in context: A083057 A099028 A357521 * A198197 A203400 A077869

Adjacent sequences: A279642 A279643 A279644 * A279646 A279647 A279648

Keyword

nonn,easy,look

Author

Paolo P. Lava, Dec 16 2016

Status

approved