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%I #19 Oct 19 2023 09:07:51
%S 1,2,3,6,13,25,50,101,201,402,804,1608,3217,6434,12868,25736,51472,
%T 102944,205887,411775,823550,1647099,3294199,6588397,13176795,
%U 26353589,52707179,105414357,210828714,421657428,843314857,1686629713,3373259426,6746518852
%N Nearest integer to 2^n*Pi/4.
%C a(n)/2^n is the closest approximation to Pi/4 using n+1 bits, where the most significant one has weight 1.
%e The first approximations to Pi/4 are given in the following table.
%e ---+--------+-----------------------+----------------
%e n -+- a(n) -+- a(n)/2^n (n+1 bits) --- decimal value
%e ---+--------+-----------------------+----------------
%e 0 -+- 1 ----+------ 1 --------------+- 1
%e 1 -+- 2 ----+------ 1.0 ------------+- 1
%e 2 -+- 3 ----+------ 0.11 -----------+- 0.75
%e 3 -+- 6 ----+------ 0.110 ----------+- 0.75
%e 4 -+- 13 ---+------ 0.1101 ---------+- 0.8125
%e 5 -+- 25 ---+------ 0.11001 --------+- 0.78125
%e 6 -+- 50 ---+------ 0.110010 -------+- 0.78125
%e 7 -+- 101 --+------ 0.1100101 ------+- 0.7890625
%e 8 -+- 201 --+------ 0.11001001 -----+- 0.78515625
%e ------------------------------- Pi/4 = 0.785398...
%t Round[2^Range[0,40] Pi/4] (* _Harvey P. Dale_, Apr 06 2013 *)
%o (PARI) a(n)=round(2^n*Pi/4)
%Y a(n)-2a(n-1)=A155482(-n), Cf. A068425.
%Y Cf. A121349. [_R. J. Mathar_, Feb 08 2009]
%Y Cf. A003881.
%K nonn
%O 0,2
%A _Jaume Oliver Lafont_, Feb 01 2009
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