A289494 -id:A289494

A289493

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

+10
9

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

FORMULA

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

PROG

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

CROSSREFS

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

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

KEYWORD

nonn

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289495

Number of primes in the interval [4n, 5n].

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

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

PROG

(PARI) a(n) = primepi(5*n) - primepi(4*n); \\ Michel Marcus, Jul 08 2017

CROSSREFS

Cf. A035250, A289493, A289494, A289496, A289497, A289498, A289499, A289500.

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289496

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

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,7

LINKS

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

MATHEMATICA

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289497

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

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

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

PROG

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289498

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

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289499

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

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 07 2017

STATUS

approved

A289500

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

+10
8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

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

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

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 *)

PROG

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

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

CROSSREFS

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

Cf. A038801.

KEYWORD

nonn,easy

AUTHOR

FUNG Cheok Yin, Jul 12 2017

STATUS

approved