

A024810


a(n) = floor( tan(m*Pi/2) ), where m = 1  2^(n).


2



1, 2, 5, 10, 20, 40, 81, 162, 325, 651, 1303, 2607, 5215, 10430, 20860, 41721, 83443, 166886, 333772, 667544, 1335088, 2670176, 5340353, 10680707, 21361414, 42722829, 85445659, 170891318, 341782637, 683565275, 1367130551, 2734261102, 5468522204, 10937044409
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OFFSET

1,2


COMMENTS

Geometrically, each term of the sequence represents the integer part of the distance between opposite vertices and also edges of even sided polygons, each of which has double the number of sides of the previous, starting with a square of unit length.  Torlach Rush, Feb 21 2014
a(n) is the greatest integer k such that k/2^n < 2/Pi.  Clark Kimberling, Oct 10 2017
Number of roots of sin(1/x) = 0 in interval 1/2^(n+1) < x < 1.  Hugo Pfoertner, Oct 24 2019
Or simply: number of zeros of sin(x) in the range [1, 2^(n+1)].  M. F. Hasler, Oct 25 2019


LINKS



FORMULA

a(n) = floor( 1 / tan( Pi / 2^(n+1) )).  Michael Somos, Feb 24 2014


MATHEMATICA

Table[Floor[Tan[(1  2^(n)) Pi/2]], {n, 1, 40}] (* Vincenzo Librandi, Feb 26 2014 *)


PROG

(PARI) a(n) = floor(tan((1  2^(n))*Pi/2)) \\ Michel Marcus, Mar 23 2013


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



