cp's OEIS Frontend

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.

%I A066880 #16 Dec 27 2023 20:41:07
%S A066880 2,3,6,7,14,15,30,31,62,63,126,127,254,255,510,511,1022,1023,2046,
%T A066880 2047,4094,4095,8190,8191,16382,16383,32766,32767,65534,65535,131070,
%U A066880 131071,262142,262143,524286,524287,1048574,1048575,2097150,2097151,4194302,4194303
%N 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.
%C A066880 This sequence consists of all numbers of the form 2^k - 2, 2^k - 1, where k >= 2.
%H A066880 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-2).
%F A066880 From _Alois P. Heinz_, Dec 27 2023: (Start)
%F A066880 G.f.: -x*(2*x^3-3*x-2)/((x-1)*(x+1)*(2*x^2-1)).
%F A066880 a(n) = 2^floor((n+3)/2)-1-(n mod 2). (End)
%e A066880 The sequence corresponding to 14 is 7, 3, 1, all of whose terms are odd. So 14 is a term of the sequence.
%t A066880 atsoQ[n_]:=AllTrue[Rest[NestWhileList[Floor[#/2]&,n,#>1&]],OddQ]; Select[Range[2,42*10^5],atsoQ] (* _Harvey P. Dale_, Dec 27 2023 *)
%Y A066880 Cf. A075427.
%K A066880 easy,nonn
%O A066880 1,1
%A A066880 _Joseph L. Pe_, Jan 21 2002
%E A066880 More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002