|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
easy,frac,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|