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

Author

Peter Luschny, May 03 2009

Keywords

• easy
• frac
• nonn

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

Crossrefs

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

Programs

Magma

[Numerator((2*n+1)/(2^(2*n+1)-1)): n in [0..70]]; // Vincenzo Librandi, Apr 25 2018

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 *)

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

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