A141602 - OEIS

%I #24 Sep 21 2024 08:41:20

%S 2,2,3,5,9,15,26,46,82,147,268,492,909,1688,3151,5909,11123,21010,

%T 39809,75638,144073,275050,526182,1008516,1936352,3723754,7171675,

%U 13831089,26708310,51636066,99940774,193635250,375535031,728979766,1416303547

%N Integer part of 2^n/log(2^n).

%C 2^n/log(2^n) is an approximation to the number of primes < 2^n.

%H G. C. Greubel, <a href="/A141602/b141602.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A050500(2^n) = floor(2^n*A007525/n) >= A000799(n). - _R. J. Mathar_, Jan 05 2009

%t Floor[2^#/Log[2^#]]&/@Range[40] (* _Harvey P. Dale_, Mar 11 2013 *)

%o (PARI) g(n) = for(x=1,n,y=floor(2^x/log(2^x));print1(y","))

%o (PARI) a(n) = 2^n\log(2^n); \\ _Michel Marcus_, Feb 24 2021

%o (Magma)

%o A141602:= func< n | Floor(2^n/(n*Log(2))) >;

%o [A141602(n): n in [1..40]]; // _G. C. Greubel_, Sep 21 2024

%o (SageMath)

%o def A141602(n): return int(2^n/(n*log(2)))

%o [A141602(n) for n in range(1,41)] # _G. C. Greubel_, Sep 21 2024

%Y Cf. A000799, A007525, A050500, A185192.

%K nonn

%O 1,1

%A _Cino Hilliard_, Aug 21 2008