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A251482
a(n) = floor(prime(n)/log(n)) + ceiling(prime(n)/log(prime(n))) - 2*n, n >=2.
1
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
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
KEYWORD
sign,easy,changed
AUTHOR
Freimut Marschner, Dec 07 2014
STATUS
approved