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

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, 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, 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

Offset

2,1

Comments

The prime number theorem implies prime(n)/log(prime(n)) < n < prime(n)/log(n), n >= 2. From this follows a(n).

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Formula

a(n) = A085581(n) + (A086861(n) + 1) - 2*n.

Example

a(4) = floor(5.04...) + ceiling(3.59...) - 2*4 = 5 + 4 - 2*4 = 1.

Mathematica

a251482[n_Integer] :=
Floor[Prime[#]/Log[#]] + Ceiling[Prime[#]/Log[Prime[#]]] - 2 # & /@
Range[2, n]; a251482[100] (* Michael De Vlieger, Dec 15 2014 *)

Prog

(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
(Magma) [Floor(NthPrime(n)/Log(n)) + Ceiling(NthPrime(n)/Log(NthPrime(n))) - 2*n: n in [2..100]]; // Vincenzo Librandi, Mar 25 2015

Crossrefs

Cf. A086861 (floor(prime(n)/log(prime(n)))), A085581 (floor(prime(n)/log(n)).

Cf. A087724 (-PrimePi(n) + floor(prime(n)/log(n)) - 2), A000720 (pi(n)).

Cf. A060715 (Number of primes between n and 2n exclusive).

Sequence in context: A129172 A355693 A318291 * A357477 A172083 A337199

Adjacent sequences: A251479 A251480 A251481 * A251483 A251484 A251485

Keyword

sign,easy

Author

Freimut Marschner, Dec 07 2014

Status

approved