A160144 Numerator of (2*n+1)/(2^(2*n+1)-1).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 3, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 9, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 15, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127

Offset

0,2

Comments

This first differs from A005408 (the odd numbers 2n+1) at a(10). The sequence of differences is A160145. This explains the similarity of A009843 (expansion of x/cos(x)) and A160143. A156769 describes a similar companion to A036279 (expansion of tan(x)).

Links

Altug Alkan, Table of n, a(n) for n = 0..10000

Maple

seq(numer((2*n+1)/(4^(2*n+1)-2^(2*n+1))), n=0..32);
seq(numer((2*n+1)/(2^(2*n+1)-1)), n=0..50); # Altug Alkan, Apr 21 2018

Mathematica

Array[Numerator[(2 # + 1)/(2^(2 # + 1) - 1)] &, 64, 0] (* Michael De Vlieger, Apr 21 2018 *)

Prog

(PARI) vector(80, n, n--; numerator((2*n+1)/(4^(2*n+1)-2^(2*n+1)))) \\ Michel Marcus, Jan 31 2015
(PARI) forstep(k=1, 1e3, 2, print1(numerator(k/(2^k-1)), ", ")); \\ Altug Alkan, Apr 21 2018
(Magma) [Numerator((2*n+1)/(2^(2*n+1)-1)): n in [0..70]]; // Vincenzo Librandi, Apr 25 2018

Crossrefs

Cf. A005408, A009843, A036279, A156769, A160143, A160145, A303449 (denominators).

Sequence in context: A094042 A248196 A245234 * A237292 A098729 A160939

Adjacent sequences: A160141 A160142 A160143 * A160145 A160146 A160147

Keyword

easy,frac,nonn

Author

Peter Luschny, May 03 2009

Extensions

More terms from Michel Marcus, Jan 31 2015

Name simplified by Altug Alkan, Apr 21 2018

Further edited by N. J. A. Sloane, Apr 24 2018

Status

approved