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Decimal expansion of 58291/21444.
3

%I #29 Feb 23 2024 13:08:34

%S 2,7,1,8,2,8,9,4,9,8,2,2,7,9,4,2,5,4,8,0,3,2,0,8,3,5,6,6,4,9,8,7,8,7,

%T 5,3,9,6,3,8,1,2,7,2,1,5,0,7,1,8,1,4,9,5,9,8,9,5,5,4,1,8,7,6,5,1,5,5,

%U 7,5,4,5,2,3,4,0,9,8,1,1,6,0,2,3,1,3,0,0

%N Decimal expansion of 58291/21444.

%C It is a rational approximation of e having an error less than 0.0003% provided by Charles Hermite in 1874 (see Hermite and Maor), where the error is calculated by abs(58291/21444-e)/e and expressed in percent.

%C Periodic with a period length of 893. - _Ray Chandler_, Jan 19 2024

%D Eli Maor, e: The Story of a Number. Princeton, New Jersey: Princeton University Press (1994), p. 189.

%H Philip R. Brown, <a href="https://doi.org/10.1080/0020739X.2017.1352043">Approximations of e and Pi: an exploration</a>, International Journal of Mathematical Education in Science and Technology, 48:sup1, S30-S39, 2017. See p. S32.

%H Charles Hermite, <a href="https://archive.org/details/13Hermite/page/n29/mode/2up">Sur la fonction exponentielle</a>, Gauthier-Villars, Paris, 1874.

%H <a href="/index/Ea">Index entries for sequences related to the number e</a>

%H <a href="/index/Rec#order_893">Index entries for linear recurrences with constant coefficients</a>, order 893.

%e 2.7182894982279425480320835664987875396381272...

%t Flatten[First[RealDigits[58291/21444,10,100]]]

%Y Cf. A001113, A007676, A007677, A368617, A368654, A368656.

%K nonn,cons,easy

%O 1,1

%A _Stefano Spezia_, Jan 02 2024