A097935 Number of primes that are not less than prime(n)-n and not greater than prime(n)+n.

2, 3, 4, 4, 3, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 8, 9, 9, 10, 10, 12, 10, 10, 10, 11, 11, 12, 13, 13, 12, 13, 12, 12, 14, 16, 15, 15, 14, 15, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 20, 18, 18, 20, 19, 19, 20, 21, 21, 21, 20, 21, 21, 23, 22, 23, 21, 22, 22, 22, 23, 24, 25

Offset

1,1

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000720(A014688(n)) - A000720(A014689(n)-1).

Example

a(10) = #{p prime: A000040(10)-10 <= p <= A000040(10)+10} = #{p prime: 19 <= p <= 39} = #{19,23,29,31,37} = 5.

Mathematica

a[n_] := PrimePi[Prime[n] + n] - PrimePi[Prime[n] - n - 1];
Array[a, 100] (* Jean-François Alcover, Jun 11 2019 *)

Prog

(Sage)
[len([k for k in (nth_prime(n)-n..nth_prime(n)+n) if is_prime(k)]) for n in (1..75)]  # Peter Luschny, Sep 03 2013
(PARI) a(n) = my(p=prime(n)); primepi(p+n) - primepi(p-n-1); \\ Michel Marcus, Jun 11 2019

Crossrefs

Cf. A000720, A014688, A014689.

Sequence in context: A059686 A101083 A373557 * A188940 A286549 A286551

Adjacent sequences: A097932 A097933 A097934 * A097936 A097937 A097938

Keyword

nonn

Author

Reinhard Zumkeller, Sep 05 2004

Status

approved