A120936 Number of primes in the interval [n,n+log(n)].

0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2

Offset

1,11

Comments

Soundararajan states that, on average, there is one prime in the interval [n,n+log(n)] for any number n. See A120934 for the prime n that yield new records.

Links

T. D. Noe, Table of n, a(n) for n = 1..5000

K. Soundararajan, The distribution of prime numbers

Mathematica

Table[Length[Select[Range[n, n+Log[n]], PrimeQ]], {n, 150}]

Prog

(PARI) a(n)=sum(k=n, n+log(n), isprime(k)) \\ Charles R Greathouse IV, Apr 17 2012

Crossrefs

Cf. A008407, A020497.

Sequence in context: A037906 A319394 A278347 * A335294 A214438 A173432

Adjacent sequences: A120933 A120934 A120935 * A120937 A120938 A120939

Keyword

nonn

Author

T. D. Noe, Jul 21 2006

Status

approved