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A112302
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Decimal expansion of quadratic recurrence constant sqrt(1 * sqrt(2 * sqrt(3 * sqrt(4 * ...)))).
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11
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1, 6, 6, 1, 6, 8, 7, 9, 4, 9, 6, 3, 3, 5, 9, 4, 1, 2, 1, 2, 9, 5, 8, 1, 8, 9, 2, 2, 7, 4, 9, 9, 5, 0, 7, 4, 9, 9, 6, 4, 4, 1, 8, 6, 3, 5, 0, 2, 5, 0, 6, 8, 2, 0, 8, 1, 8, 9, 7, 1, 1, 1, 6, 8, 0, 2, 5, 6, 0, 9, 0, 2, 9, 8, 2, 6, 3, 8, 3, 7, 2, 7, 9, 0, 8, 3, 6, 9, 1, 7, 6, 4, 1, 1, 4, 6, 1, 1, 6, 7, 1, 5, 5, 2, 8
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OFFSET
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1,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
J. Guillera and J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, Ramanujan J. 16 (2008) 247-270.
S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., AMS Chelsea 2000. See Appendix I. p. 348.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. 332 (2007) 292-314.
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..1000 . [From Robert G. Wilson v, Nov 05 2010]
S. Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 6.10.
M. D. Hirschhorn, A note on Somos' quadratic recurrence constant, J. Number Theory 131 (2011) 2061-2063
Cristinel Mortici, Estimating the Somos' quadratic recurrence constant, J. Number Theory 130 (2010) 2650-1657.
J. Sondow and J. Guillera, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, see page 8.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant
Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant
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FORMULA
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Product n^(1/2^n), n=1...infty. - Jonathan Sondow, Apr 07 2013
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EXAMPLE
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1.6616879496335941212958189227499507499644186350250682081897111680...
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MATHEMATICA
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RealDigits[ Fold[ N[ Sqrt[ #2*#1], 128] &, Sqrt@ 351, Reverse@ Range@ 350], 10, 111][[1]] [From Robert G. Wilson v, Nov 05 2010]
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PROG
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(PARI) {a(n) = if( n<-1, 0, n++; default( realprecision, n+2); floor( prodinf( k=1, k^2^-k)* 10^n) % 10)}
(PARI) prodinf(n=1, n^2^-n) \\ Charles R Greathouse IV, Apr 07 2013
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CROSSREFS
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Cf. A052129, A116603, A123851 - A123854.
Sequence in context: A200281 A199864 A153605 * A073012 A102522 A201672
Adjacent sequences: A112299 A112300 A112301 * A112303 A112304 A112305
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KEYWORD
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cons,nonn
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AUTHOR
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Michael Somos, Sep 02 2005
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STATUS
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approved
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