A271573 Numerator of (0 followed by A005126(n)= 2, 4, 7, ...)/2^n.

0, 1, 1, 7, 3, 21, 19, 71, 17, 265, 261, 1035, 515, 4109, 4103, 16399, 2049, 65553, 65545, 262163, 131077, 1048597, 1048587, 4194327, 1048579, 16777241, 16777229, 67108891, 33554439, 268435485, 268435471, 1073741855, 67108865, 4294967329, 4294967313

Offset

0,4

Comments

Reduced fractions: f(n) = 0, 1, 1, 7/8, 3/4, 21/32, 19/32, 71/128, 17/32, 265/512, 261/512, ... .

f(n) is an autosequence of the first kind.

Links

Robert Price, Table of n, a(n) for n = 0..101

Formula

a(n) = numerator(n/2^n + (if n<2 0 else 1)/2), a formula using Oresme numbers n/2^n. - Jean-François Alcover, Apr 28 2016 after Paul Curtz

Example

a(0), a(1), a(2), a(3), a(4), are the numerators of reduced fractions 0/1, 2/2, 4/4, 7/8, 12/16, ... .

Mathematica

Prepend[Table[Numerator[(2^n + n + 1)/2^(n + 1)], {n, 0, 100}], 0] (* Robert Price, Apr 10 2016 *)
(* Computation from Oresme numbers n/2^n: *) a[n_] := Numerator[n/2^n + If[n < 2, 0, 1]/2]; (* Jean-François Alcover, Apr 28 2016, after Paul Curtz *)

Prog

(PARI) a(n) = if(n==0, 0, numerator((2^(n-1)+n)/2^n)); \\ Altug Alkan, Apr 10 2016
(Magma) [0] cat [Numerator((2^(n-1)+n)/2^n): n in [1..40]]; // Vincenzo Librandi, Oct 13 2017

Crossrefs

Cf. A000004, A000079, A005126, A006519, A060576(n+1), A075101, A198631, A279635 (denominator).

Sequence in context: A070409 A166481 A050012 * A098231 A104716 A209313

Adjacent sequences: A271570 A271571 A271572 * A271574 A271575 A271576

Keyword

nonn,frac

Author

Paul Curtz, Apr 10 2016

Status

approved