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
Keywords
Links
- Harry J. Smith, Table of n, a(n) for n = 0..200
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
Comments