OFFSET
0,1
COMMENTS
The numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, ....
The infinite stream of digits: 0110111001011101111000...
Delete even (2nd, 4th, 6th, ...) occurrences of 0 (replaced by ~):
011~1110~10111~11110~0...
Delete odd (1st, 3rd, 5th, ...) occurrences of 1 (replaced by ~):
0~1~~1~0~10~1~~1~1~0~0...
Digits remaining define the sequence: 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, ....
MAPLE
nb := 100 ;
L := [0] ;
for n from 1 to nb do
nn := ListTools[Reverse](convert(n, base, 2)) ;
L := [op(L), op(nn)] ;
end do;
Lout := [] ;
ie :=1 ;
io :=1 ;
for i from 1 to nops(L) do
if op(i, L) =0 then
if ie>0 then
if type(ie, 'odd') then
printf("%d, ", 0) ;
end if;
end if;
ie := ie+1 ;
else
if io>0 then
if type(io, 'even') then
printf("%d, ", 1) ;
end if;
end if;
io := io+1 ;
end if;
end do: # R. J. Mathar, Dec 06 2011
MATHEMATICA
nMax = 60; bits = Join @@ Table[IntegerDigits[n, 2], {n, 0, nMax}]; pos0 = Position[bits, 0] // Flatten; even0 = Partition[pos0, 2][[All, 2]]; bits2 = ReplacePart[bits, Alternatives @@ even0 -> "~"]; pos1 = Position[bits2, 1] // Flatten; odd1 = Partition[pos1, 2][[All, 1]]; DeleteCases[ ReplacePart[ bits2, Alternatives @@ odd1 -> "~"], "~"] (* Jean-François Alcover, Nov 18 2016 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010
STATUS
approved