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

%I A030317 #24 Jul 22 2025 16:28:29
%S A030317 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,
%T A030317 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,
%U A030317 0,0,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,1,1,1,1
%N A030317 Write the odd numbers 2n - 1 in base 2 and juxtapose these binary expansions; read the result bit-by-bit.
%e A030317 1 in binary is 1.
%e A030317 3 in binary is 11.
%e A030317 5 in binary is 101.
%e A030317 7 in binary is 111.
%e A030317 9 in binary is 1001.
%e A030317 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.
%p A030317 twon := 1 :
%p A030317 dig := 1:
%p A030317 A030317 := proc()
%p A030317     global twon,dig ;
%p A030317     local a,dgs;
%p A030317     dgs := convert(twon,base,2) ;
%p A030317     a := op(-dig,%) ;
%p A030317     if dig = nops(dgs) then
%p A030317         twon := twon+2 ;
%p A030317         dig :=1 ;
%p A030317     else
%p A030317         dig := dig+1 ;
%p A030317     end if;
%p A030317     return a;
%p A030317 end proc:
%p A030317 seq(A030317(),n=1..100) ; # _R. J. Mathar_, Jul 22 2025
%t A030317 Flatten[Table[IntegerDigits[2n - 1, 2], {n, 50}]] (* _Harvey P. Dale_, Aug 06 2013 *)
%o A030317 (Scala) (1 to 31 by 2).map(Integer.toString(_, 2)).mkString.split("").map(Integer.parseInt(_)).toList // _Alonso del Arte_, Feb 10 2020
%Y A030317 Cf. A099821 (odd positive integers in base 2).
%K A030317 nonn,base,easy
%O A030317 1,1
%A A030317 _Clark Kimberling_