A064780 Number of times n occurs in A000195.

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, 336318631173, 914208823690, 2485077232853

Offset: 0

Author

Santi Spadaro, Oct 19 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A000195, A248873.

Programs

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 *)

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

Formula

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

Limit_{n->oo} 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

Extensions

More terms from Vladeta Jovovic, Oct 20 2001