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A002852 Continued fraction for Euler's constant (or Euler-Mascheroni 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 (list; graph; refs; listen; history; text; internal format)
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.

K. Y. Choong, D. E. Daykin and C. R. Rathbone, Rational approximations to pi, Math. Comp., 25 (1971), 387-392.

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 275-281.

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].

Jeffrey C. Lagarias, Euler's constant: Euler's work and modern developments, Bull. Amer. Math. Soc., 50 (2013), 527-628.

J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 71 (1998), 219-220.

J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003), 3335-3344.

J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005), 61-65.

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), 1-8.

J. Sondow and W. Zudilin, Euler's constant, q-logarithms and formulas of Ramanujan and Gosper, Ramanujan J. 12 (2006), 225-244.

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant

Eric Weisstein's World of Mathematics, Euler-Mascheroni 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]

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: A088980 A208548 A157333 * A188440 A216327 A099875

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

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Last modified April 19 00:07 EDT 2014. Contains 240735 sequences.