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A065445 Decimal expansion of Product{k=0..inf} (1+1/2^(2k))^(1/2). 3
1, 6, 4, 6, 7, 6, 0, 2, 5, 8, 1, 2, 1, 0, 6, 5, 6, 4, 8, 3, 6, 6, 0, 5, 1, 2, 2, 2, 2, 8, 2, 2, 9, 8, 4, 3, 5, 6, 5, 2, 3, 7, 6, 7, 2, 5, 7, 0, 1, 0, 2, 7, 4, 0, 9, 0, 1, 2, 4, 0, 5, 3, 1, 7, 5, 5, 1, 7, 2, 8, 1, 6, 2, 4, 3, 9, 1, 4, 1, 3, 7, 2, 1, 6, 1, 8, 8, 6, 9, 3, 9, 9, 9, 0, 7, 6, 5, 6, 4, 3, 5, 6, 6, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
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]

EXAMPLE

1.646760258121065648366051222282298435652376725701027409...

MAPLE

evalf(product((1+1/2^(2k))^(1/2), k=0..infinity), 120) # Vaclav Kotesovec, Sep 20 2014

MATHEMATICA

N[ Product[ Sqrt[ (1 + 1/2^(2k) ) ], {k, 0, Infinity} ], 500 ]

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

Cf. A065045.

Sequence in context: A198235 A226294 A176000 * A216184 A164293 A141796

Adjacent sequences:  A065442 A065443 A065444 * A065446 A065447 A065448

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

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Last modified September 17 10:52 EDT 2019. Contains 327129 sequences. (Running on oeis4.)