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A155996
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Nearest integer to 2^n*Pi/4.
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2
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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, 6746518852
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OFFSET
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0,2
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COMMENTS
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a(n)/2^n is the closest approximation to Pi/4 using n+1 bits, where the most significant one has weight 1.
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LINKS
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EXAMPLE
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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...
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MATHEMATICA
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PROG
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(PARI) a(n)=round(2^n*Pi/4)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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