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Search: id:A001113
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| A001113 |
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Decimal expansion of e.
(Formerly M1727 N0684)
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+0
182
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| 2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3, 5, 2, 6, 6, 2, 4, 9, 7, 7, 5, 7, 2, 4, 7, 0, 9, 3, 6, 9, 9, 9, 5, 9, 5, 7, 4, 9, 6, 6, 9, 6, 7, 6, 2, 7, 7, 2, 4, 0, 7, 6, 6, 3, 0, 3, 5, 3, 5, 4, 7, 5, 9, 4, 5, 7, 1, 3, 8, 2, 1, 7, 8, 5, 2, 5, 1, 6, 6, 4, 2, 7, 4, 2, 7, 4, 6
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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e is sometimes called Euler's constant, also Napier's constant.
Also, decimal expansion of sinh(1)+cosh(1) - Mohammad K. Azarian (azarian(AT)evansville.edu), Aug 15 2006
If m and n are any integers with n > 1, then |e - m/n| > 1/(S(n)+1)!, where S(n) = A002034(n) is the smallest number such that n divides S(n)!. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 04 2006
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3.
E. Maor, e: The Story of a Number, Princton Univ. Press, 1994.
G. W. Reitwiesner, An ENIAC determination of pi and e to more than 2000 decimal places. Math. Tables and Other Aids to Computation 4, (1950). 11-15.
D. Shanks and J. W. Wrench, Jr., Calculation of e to 100,000 decimals, Math. Comp., 23 (1969), 679-680.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 52.
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LINKS
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N. J. A. Sloane, Table of 50000 digits of e labeled from 0 to 49999 [based on the ICON Project link below]
Dave's Math Tables, e
X. Gourdon, Plouffe's Inverter, e to 1.250 billion digits
X. Gourdon and P. Sebah, The constant e and its computation
ICON Project, e to 50000 places
R. Nemiroff and J. Bonnell, The first 5 million digits of the number e
J. J. O'Connor & E. F. Robertson, The number e
S. Plouffe, A million digits
E. Sandifer, How Euler Did It, Who proved e is irrational?
G. Villemin's Almanach of Numbers, Constant"e"
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Uniform Sum Distribution
Eric Weisstein's World of Mathematics, Factorial Sums
Wikipedia, E(mathematical constant
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FORMULA
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e = Sum_{k >= 0} 1/k! = lim_{x -> 0} (1+x)^(1/x).
e is the unique positive root of the equation Integral_{u = 1..x} du/u = 1.
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EXAMPLE
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2.71828182845904523536028747135266249775724709369995957496696762772407663\
0353547594571382178525166427427466391932003059921817413596629043572900334\
295260595630738132328627943490763233829880753195251019...
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MAPLE
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Digits := 200: it := evalf((exp(1))/10, 200): for i from 1 to 200 do printf(`%d, `, floor(10*it)): it := 10*it-floor(10*it): od:
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MATHEMATICA
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a := N[E, 500]; For[n = 1, n < 250, n++, Print[Floor[10^(n - 1)*a] - Floor[10^(n - 2)*a]*10]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 17 2006
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CROSSREFS
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Cf. A002034, A122214, A122215, A122216, A122217, A122416, A122417.
Sequence in context: A021372 A111714 A060302 this_sequence A094121 A105178 A112257
Adjacent sequences: A001110 A001111 A001112 this_sequence A001114 A001115 A001116
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KEYWORD
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nonn,cons,nice,core
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AUTHOR
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njas
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EXTENSIONS
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Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 13 2001
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