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A064780 Number of times n occurs in A000195.

%I A064780 #38 Jul 03 2025 02:21:02
%S A064780 2,5,13,34,94,255,693,1884,5123,13923,37848,102880,279659,760191,
%T A064780 2066413,5617093,15268842,41505017,112822331,306682895,833650539,
%U A064780 2266097112,6159890600,16744318683,45515777208,123724710091,336318631173,914208823690,2485077232853
%N A064780 Number of times n occurs in A000195.
%H A064780 Harry J. Smith, <a href="/A064780/b064780.txt">Table of n, a(n) for n = 0..200</a>
%F A064780 a(n) = floor(exp(n+1))-floor(exp(n)), n>0.
%F A064780 Limit_{n->oo} a(n+1)/a(n) = e. - _Franz Vrabec_, Nov 29 2014
%F A064780 e^(n+1)-e^n-1 < A248873(n) <= a(n) < e^(n+1)-e^n+1. - _Danny Rorabaugh_, Mar 13 2015
%p A064780 floorexp:= proc(n) local j,s,t;
%p A064780   s:= 0;
%p A064780   t:= 1;
%p A064780   for j from 0 do
%p A064780     s:= s+t;
%p A064780     if j > n and t*n/(j+1-n) < 1 - frac(s) then
%p A064780        return floor(s)
%p A064780     fi;
%p A064780     t:= t*n/(j+1);
%p A064780   od
%p A064780 end proc:
%p A064780 B:= [0, seq(floorexp(i),i=1..101)]:
%p A064780 B[2..-1] - B[1..-2]; # _Robert Israel_, Mar 03 2016
%t A064780 lista = Table[Floor[Log[n]], {n, 10000000}]; Table[Length@Cases[lista, i], {i, 0, 15}] (* _José María Grau Ribas_, May 16 2013 *)
%t A064780 f[n_] := Floor[ Exp[n + 1]] - Floor[ Exp[ n]]; f[0] = 2; Array[f, 26, 0] (* _Robert G. Wilson v_, Mar 15 2015 *)
%o A064780 (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
%Y A064780 Cf. A000195, A248873.
%K A064780 nonn
%O A064780 0,1
%A A064780 _Santi Spadaro_, Oct 19 2001
%E A064780 More terms from _Vladeta Jovovic_, Oct 20 2001