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A273413
Decimal expansion of Product_{k>=0} (1 + 1/2^(2k))^(-1/2).
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
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
KEYWORD
nonn,cons
AUTHOR
Jeremy Tan, May 22 2016
STATUS
approved