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A064780 Number of times n occurs in A000195. 3
2, 5, 13, 34, 94, 255, 693, 1884, 5123, 13923, 37848, 102880, 279659, 760191, 2066413, 5617093, 15268842, 41505017, 112822331, 306682895, 833650539, 2266097112, 6159890600, 16744318683, 45515777208, 123724710091 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Lim_{n->infinity} a(n+1)/a(n) = e. - Franz Vrabec, Nov 29 2014

e^(n+1)-e^n-1 < A248873(n) <= a(n) < e^(n+1)-e^n+1. - Danny Rorabaugh, Mar 13 2015

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..200

FORMULA

a(n) = floor(exp(n+1))-floor(exp(n)), n>0.

MAPLE

floorexp:= proc(n) local j, s, t;

  s:= 0;

  t:= 1;

  for j from 0 do

    s:= s+t;

    if j > n and t*n/(j+1-n) < 1 - frac(s) then

       return floor(s)

    fi;

    t:= t*n/(j+1);

  od

end proc:

B:= [0, seq(floorexp(i), i=1..101)]:

B[2..-1] - B[1..-2]; # Robert Israel, Mar 03 2016

MATHEMATICA

lista = Table[Floor[Log[n]], {n, 10000000}]; Table[Length@Cases[lista, i], {i, 0, 15}] (* José María Grau Ribas, May 16 2013 *)

f[n_] := Floor[ Exp[n + 1]] - Floor[ Exp[ n]]; f[0] = 2; Array[f, 26, 0] (* Robert G. Wilson v, Mar 15 2015 *)

PROG

(PARI) { default(realprecision, 100); for (n=0, 200, if (n, a=floor(exp(n + 1)) - floor(exp(n)), a=2); write("b064780.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 25 2009

CROSSREFS

Cf. A000195, A248873.

Sequence in context: A261237 A318229 A186236 * A148289 A148290 A029885

Adjacent sequences:  A064777 A064778 A064779 * A064781 A064782 A064783

KEYWORD

nonn

AUTHOR

Santi Spadaro, Oct 19 2001

EXTENSIONS

More terms from Vladeta Jovovic, Oct 20 2001

STATUS

approved

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Last modified February 27 21:03 EST 2020. Contains 332309 sequences. (Running on oeis4.)