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

Author

T. D. Noe, Jul 21 2006

Keywords

• nonn

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

Crossrefs

Cf. A008407, A020497.

Programs

Mathematica

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

PARI

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