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Number of primes that are not less than prime(n)-n and not greater than prime(n)+n.
5

%I #19 Jun 18 2019 03:29:29

%S 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,

%T 13,13,12,13,12,12,14,16,15,15,14,15,17,17,17,17,17,18,18,19,19,19,20,

%U 18,18,20,19,19,20,21,21,21,20,21,21,23,22,23,21,22,22,22,23,24,25

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

%H R. Zumkeller, <a href="/A097935/b097935.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t a[n_] := PrimePi[Prime[n] + n] - PrimePi[Prime[n] - n - 1];

%t Array[a, 100] (* _Jean-François Alcover_, Jun 11 2019 *)

%o (Sage)

%o [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

%o (PARI) a(n) = my(p=prime(n)); primepi(p+n) - primepi(p-n-1); \\ _Michel Marcus_, Jun 11 2019

%Y Cf. A000720, A014688, A014689.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 05 2004