A289495 -id:A289495 - cp's OEIS frontend

A289493 Number of primes in the interval [2n, 3n].

2, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 9, 10, 10, 9, 10, 10, 9, 10, 9, 9, 10, 9, 10, 10, 11, 12, 12, 12, 12, 13, 13, 14, 14, 13, 12, 13, 13, 13, 13, 13, 13, 14, 15, 14, 15

Offset: 1

FUNG Cheok Yin, Jul 07 2017

nonn

FUNG Cheok Yin, Table of n, a(n) for n = 1..10000
Mohamed El Bachraoui, Primes in the interval [2n, 3n] (2006)
FUNG Cheok Yin, C++ program

Cf. A035250, A289494, A289495, A289496, A289497, A289498, A289499, A289500.

Cf. A000720 (PrimePi), A101985 (numbers occurring here exactly once).

A289493(n)=primepi(3*n)-if(n>1,primepi(2*n)) \\ M. F. Hasler, Sep 29 2019

a(n) = A000720(3n) - A000720(2n), for n > 1. - M. F. Hasler, Sep 29 2019

A289494 Number of primes in the interval [3n, 4n].

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 3, 4, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 6, 5, 6, 6, 7, 8, 9, 8, 8, 9, 9, 8, 9, 10, 11, 10, 10, 10, 10, 9, 9, 10, 10, 11, 11, 11, 11, 12, 11, 11, 11, 10, 12, 12, 13, 14, 14, 14, 15, 14

Offset: 1

FUNG Cheok Yin, Jul 07 2017

FUNG Cheok Yin, Table of n, a(n) for n = 1..10000
Andy Loo, On the Primes in the Interval [3n, 4n], arXiv:1110.2377 [math.NT], 2011.

Cf. A035250, A289493, A289495, A289496, A289497, A289498, A289499, A289500.

Join[{1},Rest[Table[PrimePi[4n]-PrimePi[3n],{n,80}]]] (* Harvey P. Dale, Dec 30 2024 *)

A289496 Number of primes in the interval [5n, 6n].

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 3, 3, 4, 3, 2, 3, 4, 6, 5, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 6, 6, 5, 7, 7, 6, 7, 8, 8, 9, 9, 8, 9, 9, 9, 9, 8, 9, 10, 9, 8, 8, 7, 8, 9, 10, 10, 10, 9, 10, 11, 11, 12, 11, 12, 11, 11, 11, 12, 13, 13, 12, 13, 14, 14, 14

Offset: 1

FUNG Cheok Yin, Jul 07 2017

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

Cf. A035250, A289493, A289494, A289495, A289497, A289498, A289499, A289500.

Table[Count[Range[5n,6n],?PrimeQ],{n,80}] (* _Harvey P. Dale, Sep 07 2017 *)

A289497 Number of primes in the interval [6n, 7n].

Original entry on oeis.org

1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 5, 4, 2, 2, 4, 4, 4, 4, 5, 5, 6, 5, 5, 6, 5, 5, 5, 5, 5, 7, 7, 8, 7, 7, 7, 8, 8, 7, 7, 8, 8, 6, 6, 6, 8, 9, 8, 7, 8, 10, 10, 10, 10, 9, 9, 10, 11, 11, 10, 10, 12, 12, 12, 12, 12, 12, 13, 13, 11, 12, 12, 10, 9, 10, 10

Offset: 1

FUNG Cheok Yin, Jul 07 2017

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

Cf. A035250, A289493, A289494, A289495, A289496, A289498, A289499, A289500.

a(n) = primepi(7*n) - primepi(6*n); \\ Michel Marcus, Jul 08 2017

A289498 Number of primes in the interval [7n, 8n].

Original entry on oeis.org

1, 0, 1, 2, 1, 2, 1, 2, 2, 3, 2, 1, 3, 4, 3, 2, 2, 4, 4, 3, 5, 4, 5, 4, 6, 4, 5, 4, 4, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 7, 5, 5, 6, 7, 7, 7, 8, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 11, 11, 11, 11, 10, 11, 11, 10, 10, 8, 9, 9, 9, 9, 9, 9, 10, 10, 12, 13, 14, 14, 13

Offset: 1

FUNG Cheok Yin, Jul 07 2017

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

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289499, A289500.

A289499 Number of primes in the interval [8n, 9n].

Original entry on oeis.org

0, 1, 0, 0, 2, 1, 2, 2, 2, 2, 2, 4, 3, 1, 2, 3, 4, 3, 3, 4, 3, 5, 4, 4, 2, 5, 6, 6, 5, 5, 6, 7, 6, 4, 6, 5, 5, 6, 6, 6, 7, 7, 8, 7, 7, 7, 8, 7, 8, 9, 9, 11, 9, 9, 9, 10, 10, 8, 8, 7, 8, 8, 7, 8, 9, 9, 11, 11, 13, 12, 12, 13, 13, 14, 13, 13, 13, 12, 12, 13

Offset: 1

FUNG Cheok Yin, Jul 07 2017

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

Cf. A035250, A289493, A289494, A289495, A289496, A289497, A289498, A289500.

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

Original entry on oeis.org

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

FUNG Cheok Yin, Jul 12 2017

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

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

Cf. A038801.

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

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

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

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

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

cp's OEIS Frontend

A289493 Number of primes in the interval [2n, 3n].

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PARI

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A289494 Number of primes in the interval [3n, 4n].

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Mathematica

A289496 Number of primes in the interval [5n, 6n].

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Mathematica

A289497 Number of primes in the interval [6n, 7n].

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Programs

PARI

A289498 Number of primes in the interval [7n, 8n].

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A289499 Number of primes in the interval [8n, 9n].

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

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Programs

Magma

Maple

Mathematica

PARI

Formula