%I A002852 M0097 N0034
%S A002852 0,1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,3,7,1,7,1,1,5,1,49,4,1,
%T A002852 65,1,4,7,11,1,399,2,1,3,2,1,2,1,5,3,2,1,10,1,1,1,1,2,1,1,3,1,4,1,1,2,
%U A002852 5,1,3,6,2,1,2,1,1,1,2,1,3,16,8,1,1,2,16,6,1,2,2,1,7,2,1,1,1,3,1,2,1,2
%N A002852 Continued fraction for Euler's constant (or Euler-Mascheroni constant) 
               gamma.
%D A002852 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 3.
%D A002852 K. Y. Choong, D. E. Daykin and C. R. Rathbone, Rational approximations 
               to pi, Math. Comp., 25 (1971), 387-392.
%D A002852 K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions 
               for pi and gamma, Math. Comp., 25 (1971), 403.
%D A002852 D. E. Knuth, Euler's constant to 1271 places. Math. Comp. 16 1962 275-281.
%D A002852 R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic 
               Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959.
%D A002852 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002852 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002852 J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an 
               analogue of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 
               61-65.
%D A002852 J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. 
               Math. Soc. 131 (2003) 3335-3344.
%D A002852 J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 
               71 (1998) 219-220.
%H A002852 T. D. Noe, <a href="b002852.txt">Table of n, a(n) for n=0..10000</a>
%H A002852 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A002852 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Euler-MascheroniConstant.html">Link to a section of The World of 
               Mathematics.</a>
%H A002852 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A002852 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%H A002852 J. Sondow, <a href="http://arXiv.org/abs/math.CA/0306008">An infinite 
               product for e^gamma via hypergeometric formulas for Euler's constant, 
               gamma</a>
%H A002852 J. Sondow, <a href="http://arXiv.org/abs/math.NT/0211075">A hypergeometric 
               approach, via linear forms involving logarithms, to irrationality 
               criteria for Euler's constant</a>
%H A002852 J. Sondow and W. Zudilin, <a href="http://arXiv.org/abs/math.NT/0304021">
               Euler's constant, q-logarithms and formulas of Ramanujan and Gosper</
               a>
%e A002852 0.577215664901532860606512090082402431042...
%t A002852 ContinuedFraction[ EulerGamma, 100 ]
%o A002852 (PARI) { default(realprecision, 11000); x=contfrac(Euler); for (n=0, 
               10000, write("b002852.txt", n, " ", x[n+1])); } [From Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Apr 14 2009]
%Y A002852 Cf. A001620, the decimal expansion, which has many more references.
%Y A002852 See also A073004 (exp(gamma)).
%Y A002852 Sequence in context: A088931 A088980 A157333 this_sequence A099875 A079499 
               A166235
%Y A002852 Adjacent sequences: A002849 A002850 A002851 this_sequence A002853 A002854 
               A002855
%K A002852 nonn,cofr,nice
%O A002852 0,4
%A A002852 N. J. A. Sloane (njas(AT)research.att.com).
%E A002852 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 08 2000