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

0,1

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.

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

a(n) = A000149(n+1) - A001671(n) + 1 = floor(exp(n+1)) - ceiling(exp(n)) + 1. - Rayhan Ahmed, May 21 2026

From Rayhan Ahmed, Jun 18 2026: (Start)

a(n) = A001671(n+1) - A001671(n).

Sum_{k=0..n-1} a(k) = A001671(n) - 1. (End)

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 *)
(* Alternative: *)
f[n_] := Floor[ Exp[n + 1]] - Floor[ Exp[ n]]; f[0] = 2; Array[f, 29, 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. A000149, A000195, A001671, A248873.

Sequence in context: A261237 A318229 A186236 * A368599 A148289 A148290

Adjacent sequences: A064777 A064778 A064779 * A064781 A064782 A064783

Keyword

nonn,changed

Author

Santi Spadaro, Oct 19 2001

Extensions

More terms from Vladeta Jovovic, Oct 20 2001

Status

approved