0,2

a(n)/2^n is the closest approximation to Pi/4 using n+1 bits, where the most significant one has weight 1.

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...

(PARI) a(n)=round(2^n*Pi/4)

a(n)-2a(n-1)=A155482(-n), Cf. A068425.

Cf. A121349. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2009]

Sequence in context: A111503 A075530 A032061 this_sequence A018274 A018775 A086514

Adjacent sequences: A155993 A155994 A155995 this_sequence A155997 A155998 A155999

nonn

Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 01 2009