A273413 Decimal expansion of Product_{k>=0} (1 + 1/2^(2k))^(-1/2).

6, 0, 7, 2, 5, 2, 9, 3, 5, 0, 0, 8, 8, 8, 1, 2, 5, 6, 1, 6, 9, 4, 4, 6, 7, 5, 2, 5, 0, 4, 9, 2, 8, 2, 6, 3, 1, 1, 2, 3, 9, 0, 8, 5, 2, 1, 5, 0, 0, 8, 9, 7, 7, 2, 4, 5, 6, 9, 7, 6, 0, 1, 3, 1, 1, 0, 1, 4, 7, 8, 8, 1, 2, 0, 8, 4, 2, 4, 9, 0, 6, 9, 0, 6, 2, 2, 7, 4, 2, 5, 9, 0, 8, 0, 3, 8, 4, 0, 5, 2, 7, 4

Offset

0,1

Comments

This constant is multiplied into the CORDIC algorithm to obtain the correct sine or cosine. See p. 647 of the fxtbook (below).

Links

Jeremy Tan, Table of n, a(n) for n = 0..249

Joerg Arndt, Matters Computational (The Fxtbook), section 33.2

Wikipedia, CORDIC

Formula

Equals 1/A065445.

Example

0.60725293500888125616944675250492826311239085215008977245...

Prog

(PARI)
pent(z, n)= 1+sum(k=1, n, (-1)^k*(z^(k*(3*k-1)/2) + z^(k*(3*k+1)/2)));
/* == prod(n>=1, 1-z^n) via pentagonal number theorem */
N=30; u=0.25; K1=1/sqrt( 2 * pent(u^2, N)/pent(u, N) )
/* using prod(n>=1, 1+z^2) = prod(n>=1, 1-(z^2)^2)/prod(n>=1, 1-z^n) */
\\ Joerg Arndt, May 23 2016

Crossrefs

Cf. A065445.

Sequence in context: A353091 A021900 A351401 * A341906 A365163 A195432

Adjacent sequences: A273410 A273411 A273412 * A273414 A273415 A273416

Keyword

nonn,cons

Author

Jeremy Tan, May 22 2016

Status

approved