A030317 Write the odd numbers 2n - 1 in base 2 and juxtapose these binary expansions; read the result bit-by-bit.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Examples

			1 in binary is 1.
3 in binary is 11.
5 in binary is 101.
7 in binary is 111.
9 in binary is 1001.
Putting those together, we obtain 1111011111001. Then, splitting bit by bit, we get 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, the beginning of this sequence.
		

Crossrefs

Cf. A099821 (odd positive integers in base 2).

Programs

Maple

twon := 1 :
dig := 1:
A030317 := proc()
    global twon,dig ;
    local a,dgs;
    dgs := convert(twon,base,2) ;
    a := op(-dig,%) ;
    if dig = nops(dgs) then
        twon := twon+2 ;
        dig :=1 ;
    else
        dig := dig+1 ;
    end if;
    return a;
end proc:
seq(A030317(),n=1..100) ; # R. J. Mathar, Jul 22 2025

Mathematica

Flatten[Table[IntegerDigits[2n - 1, 2], {n, 50}]] (* Harvey P. Dale, Aug 06 2013 *)

Scala

(1 to 31 by 2).map(Integer.toString(, 2)).mkString.split("").map(Integer.parseInt()).toList // Alonso del Arte, Feb 10 2020