A289500 Number of primes in the interval [9n, 10n].

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, 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, 12, 11, 12, 10, 11, 12, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11

Offset: 1

Author

FUNG Cheok Yin, Jul 12 2017

Keywords

• nonn
• easy

Links

• FUNG Cheok Yin, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A038801.

Programs

Magma

[0] cat [#PrimesInInterval(9*n, 10*n): n in [2..100]]; // Vincenzo Librandi, Jul 13 2017

Maple

seq(numtheory:-pi(10*n)-numtheory:-pi(9*n),n=1..100); # Robert Israel, Jul 12 2017

Mathematica

Join[{0}, Table[PrimePi[10 n] - PrimePi[9 n], {n, 2, 100}]] (* Vincenzo Librandi, Jul 13 2017 *)

PARI

a(n) = primepi(10*n) - primepi(9*n); \\ Michel Marcus, Jul 12 2017

Formula

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