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
KEYWORD
AUTHOR
Paolo P. Lava, Dec 16 2016
STATUS
approved