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A112302 Decimal expansion of quadratic recurrence constant sqrt(1 * sqrt(2 * sqrt(3 * sqrt(4 * ...)))). 12
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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.

LINKS

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

FORMULA

Product n^(1/2^n), n=1…infty. - Jonathan Sondow, Apr 07 2013

lim_{n->infinity} A055209(n)^(1/2^(n+1)). - Petros Hadjicostas and Jonathan Sondow, Mar 22 2014

EXAMPLE

1.6616879496335941212958189227499507499644186350250682081897111680...

MATHEMATICA

RealDigits[ Fold[ N[ Sqrt[ #2*#1], 128] &, Sqrt@ 351, Reverse@ Range@ 350], 10, 111][[1]] (* Robert G. Wilson v, Nov 05 2010 *)

Exp[-Derivative[1, 0][PolyLog][0, 1/2]] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Apr 07 2014, after Jonathan Sondow *)

PROG

(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

CROSSREFS

Cf. A052129, A055209, A116603, A123851 - A123854.

Sequence in context: A200281 A199864 A153605 * A073012 A102522 A201672

Adjacent sequences:  A112299 A112300 A112301 * A112303 A112304 A112305

KEYWORD

cons,nonn

AUTHOR

Michael Somos, Sep 02 2005

STATUS

approved

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Last modified April 24 09:00 EDT 2014. Contains 240957 sequences.