

A002852


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


21



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.
The first 16695279010 terms were computed by Syed Fahad on Apr 29 2021, see link.


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

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].


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 continued fraction).


KEYWORD

nonn,cofr,nice


AUTHOR



EXTENSIONS



STATUS

approved



