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A000149
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a(n) = floor(e^n).
(Formerly M1751 N0695)
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42
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1, 2, 7, 20, 54, 148, 403, 1096, 2980, 8103, 22026, 59874, 162754, 442413, 1202604, 3269017, 8886110, 24154952, 65659969, 178482300, 485165195, 1318815734, 3584912846, 9744803446, 26489122129, 72004899337, 195729609428, 532048240601, 1446257064291
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Satisfies Benford's law [Whyman et al., 2016]. - N. J. A. Sloane, Feb 12 2017
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REFERENCES
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Federal Works Agency, Work Projects Administration for the City of NY, Tables of the Exponential Function. National Bureau of Standards, Washington, DC, 1939.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 230.
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).
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LINKS
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FORMULA
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a(n)^(1/n) converges to e because |1-a(n)/e^n|=|e^n-a(n)|/e^n < e^(-n) and so a(n)^(1/n)=(e^n*(1+o(1))^(1/n)=e*(1+o(1). - Hieronymus Fischer, Jan 22 2006
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MATHEMATICA
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PROG
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(Haskell)
a000149 = floor . (exp 1 ^)
a000149_list = let e = exp 1 in map floor $ iterate (* e) 1
(PARI) apply( A000149(n)=exp(n)\1, [0..30]) \\ An error message will say so if default(realprecision) must be increased, for large n. - M. F. Hasler, May 27 2018
(Python)
from sympy import floor, E
def a(n): return floor(E**n)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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