This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155996 Nearest integer to 2^n*Pi/4. 1
 1, 2, 3, 6, 13, 25, 50, 101, 201, 402, 804, 1608, 3217, 6434, 12868, 25736, 51472, 102944, 205887, 411775, 823550, 1647099, 3294199, 6588397, 13176795, 26353589, 52707179, 105414357, 210828714, 421657428, 843314857, 1686629713, 3373259426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)/2^n is the closest approximation to Pi/4 using n+1 bits, where the most significant one has weight 1. LINKS FORMULA a(n) = -floor(2^(-2 + n)*Pi) + floor(2^(-1 + n)*Pi), n>=0. - Mariusz Iwaniuk, Apr 30 2017 EXAMPLE The first approximations to Pi/4 are given in the following table. ---+--------+-----------------------+---------------- n -+- a(n) -+- a(n)/2^n (n+1 bits) --- decimal value ---+--------+-----------------------+---------------- 0 -+- 1 ----+------ 1 --------------+- 1 1 -+- 2 ----+------ 1.0 ------------+- 1 2 -+- 3 ----+------ 0.11 -----------+- 0.75 3 -+- 6 ----+------ 0.110 ----------+- 0.75 4 -+- 13 ---+------ 0.1101 ---------+- 0.8125 5 -+- 25 ---+------ 0.11001 --------+- 0.78125 6 -+- 50 ---+------ 0.110010 -------+- 0.78125 7 -+- 101 --+------ 0.1100101 ------+- 0.7890625 8 -+- 201 --+------ 0.11001001 -----+- 0.78515625 ------------------------------- Pi/4 = 0.785398... MATHEMATICA Round[2^Range[0, 40] Pi/4] (* Harvey P. Dale, Apr 06 2013 *) PROG (PARI) a(n)=round(2^n*Pi/4) CROSSREFS a(n)-2a(n-1)=A155482(-n), Cf. A068425. Cf. A121349. [R. J. Mathar, Feb 08 2009] Cf. A003881. Sequence in context: A239326 A075530 A032061 * A240104 A018274 A018775 Adjacent sequences:  A155993 A155994 A155995 * A155997 A155998 A155999 KEYWORD nonn AUTHOR Jaume Oliver Lafont, Feb 01 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 17:33 EST 2019. Contains 329960 sequences. (Running on oeis4.)