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A251482 a(n) = floor(prime(n)/log(n)) + ceiling(prime(n)/log(prime(n))) - 2*n, n >=2.

%I A251482 #29 Nov 12 2024 09:06:18
%S A251482 3,2,1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,-1,0,-1,0,2,0,0,-1,-2,-3,1,0,1,
%T A251482 0,1,1,1,0,0,0,1,-1,1,0,-1,-3,0,3,2,1,0,0,-2,0,1,1,1,-1,-1,-2,-3,-2,2,
%U A251482 1,-1,-1,2,1,3,2,1,1,2,1,1,1,1,2,0,2,3,1,3,1,1,0,0,1,0,-2,-3,-1,0,0,0,-1,-1,1,-1,3
%N A251482 a(n) = floor(prime(n)/log(n)) + ceiling(prime(n)/log(prime(n))) - 2*n, n >=2.
%C A251482 The prime number theorem implies prime(n)/log(prime(n)) < n < prime(n)/log(n), n >= 2. From this follows a(n).
%H A251482 Michael De Vlieger, <a href="/A251482/b251482.txt">Table of n, a(n) for n = 2..10000</a>
%F A251482 a(n) = A085581(n) + (A086861(n) + 1) - 2*n.
%e A251482 a(4) = floor(5.04...) + ceiling(3.59...) - 2*4 = 5 + 4 - 2*4 = 1.
%t A251482 a251482[n_Integer] :=
%t A251482 Floor[Prime[#]/Log[#]] + Ceiling[Prime[#]/Log[Prime[#]]] - 2 # & /@
%t A251482 Range[2, n]; a251482[100] (* _Michael De Vlieger_, Dec 15 2014 *)
%o A251482 (PARI) vector(100,n,floor(prime(n+1)/log(n+1))+ceil(prime(n+1)/log(prime(n+1)))-2*n-2) \\ _Derek Orr_, Dec 30 2014
%o A251482 (Magma) [Floor(NthPrime(n)/Log(n)) + Ceiling(NthPrime(n)/Log(NthPrime(n))) - 2*n: n in [2..100]]; // _Vincenzo Librandi_, Mar 25 2015
%Y A251482 Cf. A086861 (floor(prime(n)/log(prime(n)))), A085581 (floor(prime(n)/log(n))).
%Y A251482 Cf. A087724 (-PrimePi(n) + floor(prime(n)/log(n)) - 2), A000720 (pi(n)).
%Y A251482 Cf. A060715 (Number of primes between n and 2n exclusive).
%K A251482 sign,easy
%O A251482 2,1
%A A251482 _Freimut Marschner_, Dec 07 2014