%I #16 Sep 08 2022 08:46:19

%S 0,1,1,1,1,1,1,2,2,1,4,2,1,4,3,3,3,4,3,5,4,2,4,5,5,4,4,5,6,5,4,5,4,6,

%T 5,6,6,7,7,6,7,7,6,8,8,8,9,9,8,8,9,6,8,7,7,6,7,8,8,10,10,12,11,10,12,

%U 12,11,12,10,11,12,10,10,10,10,10,11,11,11,11,11,11

%N Number of primes in the interval [9n, 10n].

%H FUNG Cheok Yin, <a href="/A289500/b289500.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n/log(n) + (1 + log(3^18/10^10))*n/log(n)^2 + O(n/log(n)^3) as n -> infinity. - _Robert Israel_, Jul 12 2017

%p seq(numtheory:-pi(10*n)-numtheory:-pi(9*n),n=1..100); # _Robert Israel_, Jul 12 2017

%t Join[{0}, Table[PrimePi[10 n] - PrimePi[9 n], {n, 2, 100}]] (* _Vincenzo Librandi_, Jul 13 2017 *)

%o (PARI) a(n) = primepi(10*n) - primepi(9*n); \\ _Michel Marcus_, Jul 12 2017

%o (Magma) [0] cat [#PrimesInInterval(9*n, 10*n): n in [2..100]]; // _Vincenzo Librandi_, Jul 13 2017

%Y Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289499.

%Y Cf. A038801.

%K nonn,easy

%O 1,8

%A _FUNG Cheok Yin_, Jul 12 2017