OFFSET
1,2
COMMENTS
Scaling constant with CORDIC algorithm, see p. 647 of fxtbook (see link below).
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
LINKS
Harry J. Smith, Table of n, a(n) for n=1..2000
Joerg Arndt, Matters Computational (The Fxtbook), section 33.2.
Steven R. Finch, Digital Search Tree Constants [Broken link]
Steven R. Finch, Digital Search Tree Constants [From the Wayback machine]
FORMULA
Equals sqrt(A371748). - Amiram Eldar, Mar 27 2026
EXAMPLE
1.646760258121065648366051222282298435652376725701027409...
MAPLE
evalf(product((1+1/2^(2*k))^(1/2), k=0..infinity), 120); # Vaclav Kotesovec, Sep 20 2014
MATHEMATICA
RealDigits[Sqrt[Product[1 + 1/2^(2*k), {k, 0, Infinity}]], 10, 120][[1]] (* corrected by Amiram Eldar, Mar 27 2026 *)
PROG
(PARI) { default(realprecision, 2080); x=prodinf(k=0, sqrt(1 + 1/2^(2*k))); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065445.txt", n, " ", d)) } \\ Harry J. Smith, Oct 04 2009
(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; K=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) */
/* gives: 1.6467602581210... */ /* Joerg Arndt, Jan 17 2011 */
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Nov 18 2001
EXTENSIONS
More terms from Robert G. Wilson v, Nov 19 2001
Terms corrected and terms added by Harry J. Smith, Oct 04 2009
STATUS
approved