A000149 a(n) = floor(e^n). (Formerly M1751 N0695)

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

Offset

0,2

Comments

A000079(n) <= a(n) <= A000244(n); for n > 0: A064780(n) = a(n+1) - a(n). - Reinhard Zumkeller, Mar 17 2015

Satisfies Benford's law [Whyman et al., 2016]. - N. J. A. Sloane, Feb 12 2017

References

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).

Links

T. D. Noe, Table of n, a(n) for n=0..300

R. K. Guy and N. J. A. Sloane, Correspondence, 1988.

G. Whyman, N. Ohtori, E. Shulzinger and Ed. Bormashenko, Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?, Physica A: Statistical Mechanics and its Applications, 461 (2016), 595-601.

Index entries for sequences related to Benford's law

Formula

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

Mathematica

a[n_]:=Floor[E^n]; (* Vladimir Joseph Stephan Orlovsky, Dec 12 2008 *)
Floor[E^Range[0, 30]] (* Harvey P. Dale, Apr 01 2012 *)

Prog

(PARI) for(n=0, 28, print1(floor(exp(n)), ", ")); \\ Arkadiusz Wesolowski, Nov 26 2011
(Haskell)
a000149 = floor . (exp 1 ^)
a000149_list = let e = exp 1 in map floor $ iterate (* e) 1
-- Reinhard Zumkeller, Mar 17 2015
(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)
print([a(n) for n in range(29)]) # Michael S. Branicky, Jul 20 2021

Crossrefs

Bisection: A116472.

Cf. A001113, A003619, A000079, A000244, A064780 (first differences, apart from initial term).

Cf. A000227 (round e^n), A001671 (ceiling e^n).

Sequence in context: A027418 A035508 A018033 * A080041 A049681 A027120

Adjacent sequences: A000146 A000147 A000148 * A000150 A000151 A000152

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved