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A160144
Numerator of (2*n+1)/(2^(2*n+1)-1).
5
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)).
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
Sequence in context: A094042 A248196 A245234 * A237292 A098729 A160939
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