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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

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

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)

Example

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

Mathematica

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

Crossrefs

Cf. A075427.

Sequence in context: A335099 A147303 A346593 * A075427 A075426 A359041

Adjacent sequences: A066877 A066878 A066879 * A066881 A066882 A066883

Keyword

easy,nonn

Author

Joseph L. Pe, Jan 21 2002

Extensions

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

Status

approved