login
Complement of the Beatty sequence for e^(1/Pi) = A179706.
3

%I #20 Jul 17 2024 04:18:53

%S 3,7,11,14,18,22,25,29,33,36,40,44,47,51,55,58,62,66,69,73,77,80,84,

%T 88,91,95,99,102,106,110,113,117,121,124,128,132,135,139,143,146,150,

%U 154,157,161,165,168,172,176,179,183,187,190,194,198

%N Complement of the Beatty sequence for e^(1/Pi) = A179706.

%H Karl V. Keller, Jr., <a href="/A260484/b260484.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/e.html">e</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi.html">Pi</a>.

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>.

%F a(n) = floor(n*e^(1/Pi)/(e^(1/Pi)-1)).

%e For n = 5, floor(5*e^(1/Pi)/(e^(1/Pi)-1)) = 18.

%t Floor[Range[100]/(1 - Exp[-1/Pi])] (* _Paolo Xausa_, Jul 17 2024 *)

%o (Python)

%o from sympy import E, pi, floor

%o for n in range(1,101): print(floor(n*E**(1/pi)/(E**(1/pi)-1)), end=', ')

%o (PARI) vector(80, n, floor(n*exp(1/Pi)/(exp(1/Pi)-1))) \\ _Michel Marcus_, Aug 05 2015

%Y Cf. A179706 (e^(1/Pi)), A260483 (complement).

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, Jul 26 2015