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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.
1
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.
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
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