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A120936 Number of primes in the interval [n,n+log(n)]. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A214438 A173432 A101675

Adjacent sequences:  A120933 A120934 A120935 * A120937 A120938 A120939

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 21 2006

STATUS

approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)