

A073005


Decimal expansion of Gamma(1/3).


11



2, 6, 7, 8, 9, 3, 8, 5, 3, 4, 7, 0, 7, 7, 4, 7, 6, 3, 3, 6, 5, 5, 6, 9, 2, 9, 4, 0, 9, 7, 4, 6, 7, 7, 6, 4, 4, 1, 2, 8, 6, 8, 9, 3, 7, 7, 9, 5, 7, 3, 0, 1, 1, 0, 0, 9, 5, 0, 4, 2, 8, 3, 2, 7, 5, 9, 0, 4, 1, 7, 6, 1, 0, 1, 6, 7, 7, 4, 3, 8, 1, 9, 5, 4, 0, 9, 8, 2, 8, 8, 9, 0, 4, 1, 1, 8, 8, 7, 8, 9, 4, 1, 9, 1, 5
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OFFSET

1,1


COMMENTS

Nesterenko proves that this constant is transcendental (he cites Chudnovsky as the first show this); in fact it is algebraically independent of Pi and exp(sqrt(3)*Pi) over Q.  Charles R Greathouse IV, Nov 11 2013


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000
Yu V. Nesterenko, Modular functions and transcendence questions, Sbornik: Mathematics 187:9 (1996), pp. 13191348. (English translation)
Simon Plouffe, GAMMA(1/3).
Wikipedia, Particular values of the Gamma function: General rational arguments.


EXAMPLE

Gamma(1/3) = 2.6789385347077476336556929409746776441286893779573011009...


MATHEMATICA

RealDigits[ N[ Gamma[1/3], 110]][[1]]


PROG

(PARI) default(realprecision, 1080); x=gamma(1/3); for (n=1, 1000, d=floor(x); x=(xd)*10; write("b073005.txt", n, " ", d)); \\ Harry J. Smith, Apr 19 2009


CROSSREFS

Cf. decimal expansions of Gamma(1/k): A002161 (k=2), A068466 (k=4), A175380 (k=5), A175379 (k=6), A220086 (k=7), A203142 (k=8), A203140 (k=12), A203139 (k=16), A203138 (k=24), A203137 (k=48).
Cf. A073006, A203145.
Sequence in context: A140132 A186504 A096909 * A091942 A047555 A184939
Adjacent sequences: A073002 A073003 A073004 * A073006 A073007 A073008


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Aug 03 2002


EXTENSIONS

Fixed my PARI program, had n Harry J. Smith, May 19 2009


STATUS

approved



