A066880 Biased numbers: n such that all terms of the sequence f(n), f(f(n)), f(f(f(n))), ..., 1, where f(k) = floor(k/2), are odd.

2, 3, 6, 7, 14, 15, 30, 31, 62, 63, 126, 127, 254, 255, 510, 511, 1022, 1023, 2046, 2047, 4094, 4095, 8190, 8191, 16382, 16383, 32766, 32767, 65534, 65535, 131070, 131071, 262142, 262143, 524286, 524287, 1048574, 1048575, 2097150, 2097151, 4194302, 4194303

Offset: 1

Author

Joseph L. Pe, Jan 21 2002

Keywords

• easy
• nonn

Comments

This sequence consists of all numbers of the form 2^k - 2, 2^k - 1, where k >= 2.

Examples

			The sequence corresponding to 14 is 7, 3, 1, all of whose terms are odd. So 14 is a term of the sequence.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Crossrefs

Cf. A075427.

Programs

Mathematica

atsoQ[n_]:=AllTrue[Rest[NestWhileList[Floor[#/2]&,n,#>1&]],OddQ]; Select[Range[2,42*10^5],atsoQ] (* Harvey P. Dale, Dec 27 2023 *)

Formula

From Alois P. Heinz, Dec 27 2023: (Start)

G.f.: -x*(2*x^3-3*x-2)/((x-1)*(x+1)*(2*x^2-1)).

a(n) = 2^floor((n+3)/2)-1-(n mod 2). (End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002