

A002852


Continued fraction for Euler's constant (or EulerMascheroni constant) gamma.
(Formerly M0097 N0034)


18



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, 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, 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
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OFFSET

0,4


COMMENTS

The first 970258158 terms were computed by Eric Weisstein on Sep 21 2011 using a developmental version of Mathematica.
The first 4851382841 terms were computed by Eric Weisstein on Jul 22 2013 using a developmental version of Mathematica.


REFERENCES

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.
R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
K. Y. Choong, D. E. Daykin and C. R. Rathbone, Rational approximations to pi, Math. Comp., 25 (1971), 387392.
K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403.
D. E. Knuth, Euler's constant to 1271 places, Math. Comp. 16 1962 275281.
Jeffrey C. Lagarias, Euler's constant: Euler's work and modern developments, Bull. Amer. Math. Soc., 50 (2013), 527628.
J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 71 (1998), 219220.
J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003), 33353344.
J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005), 6165.
J. Sondow, An infinite product for e^gamma via hypergeometric formulas for Euler's constant, gamma
J. Sondow, A hypergeometric approach, via linear forms involving logarithms, to irrationality criteria for Euler's constant. With an Appendix by Sergey Zlobin, Math. Slovaca 59 (2009), 18.
J. Sondow and W. Zudilin, Euler's constant, qlogarithms and formulas of Ramanujan and Gosper, Ramanujan J. 12 (2006), 225244.
Eric Weisstein's World of Mathematics, EulerMascheroni Constant
Eric Weisstein's World of Mathematics, EulerMascheroni Constant Continued Fraction
G. Xiao, Contfrac
Index entries for continued fractions for constants


EXAMPLE

0.577215664901532860606512090082402431042...
0 + 1/(1 + 1/(1 + 1/(2 + 1/(1 + 1/(2 + 1/(1 + 1/(4 + 1/(3 + 1/(13 + ...


MATHEMATICA

ContinuedFraction[EulerGamma, 100]


PROG

(PARI) default(realprecision, 11000); x=contfrac(Euler); for (n=0, 10000, write("b002852.txt", n, " ", x[n+1])) \\ Harry J. Smith, Apr 14 2009
(MAGMA) ContinuedFraction(EulerGamma(100)); // Vincenzo Librandi, Oct 19 2017


CROSSREFS

Cf. A001620, the decimal expansion, which has many more references.
See also A073004 (exp(gamma)) and A094640 ("alternating Euler constant").
Cf. A033091 (incrementally largest terms), A033092 (positions of incrementally largest terms).
Cf. A033149 (positions of first occurrence of n in the c.f.).
Sequence in context: A254436 A208548 A157333 * A266081 A188440 A216327
Adjacent sequences: A002849 A002850 A002851 * A002853 A002854 A002855


KEYWORD

nonn,cofr,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Robert G. Wilson v, Dec 08 2000


STATUS

approved



