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A065445
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Decimal expansion of Product{k=0..inf} (1+1/2^(2k))^(1/2).
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2
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Scaling constant with CORDIC algorithm, see p.647 of fxtbook (see link below).
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,2000
S. R. Finch, Digital Search Tree Constants
Joerg Arndt, fxtbook.
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EXAMPLE
| 1.646760258121065648366051222282298435652376725701027409...
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MATHEMATICA
| N[ Product[ Sqrt[ (1 + 1/2^(2k) ) ], {k, 0, Infinity} ], 500 ]
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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)) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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 */
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CROSSREFS
| Cf. A065045.
Sequence in context: A176394 A198235 A176000 * A164293 A141796 A105160
Adjacent sequences: A065442 A065443 A065444 * A065446 A065447 A065448
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2001
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 19 2001
Terms corrected and terms added by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 04 2009
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