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A112302 Decimal expansion of quadratic recurrence constant sqrt(1 * sqrt(2 * sqrt(3 * sqrt(4 * ...)))). 13
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.

S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., AMS Chelsea 2000. See Appendix I. p. 348.

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

Dawei Lu and Zexi Song, Some new continued fraction estimates of the Somos' quadratic recurrence constant, Journal of Number Theory, Volume 155, October 2015, Pages 36-45.

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, arXiv:math/0506319 [math.NT], 2005-2006, see page 8.

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.

J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, arXiv:math/0610499 [math.CA], 2006.

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.

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 [This formula is incorrect, limit is equal to 1. - Vaclav Kotesovec, Jun 06 2015]

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, A123852, A123853, A123854.

Sequence in context: A199864 A153605 A247447 * 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 August 4 05:42 EDT 2015. Contains 260276 sequences.