A088683 -id:A088683 - cp's OEIS frontend

A078584 a(n) = prime(2n) - prime(2n-1).

1, 2, 2, 2, 6, 6, 2, 6, 2, 4, 6, 6, 4, 4, 4, 4, 2, 2, 6, 6, 2, 2, 2, 12, 2, 6, 10, 6, 2, 4, 10, 4, 4, 6, 2, 6, 6, 4, 8, 8, 2, 2, 4, 8, 2, 12, 4, 4, 12, 18, 10, 6, 6, 6, 2, 6, 2, 10, 4, 6, 12, 6, 10, 10, 6, 4, 6, 8, 14, 12, 10, 4, 10, 4, 4, 4, 4, 4, 10, 4, 6, 4, 6, 6, 4, 2, 2, 10, 10, 6, 4, 4, 6, 6, 22, 10

Offset: 1

Robert G. Wilson v, Nov 30 2002

First differences of A077133. Bisection of A001223.

Partition the primes in pairs starting with 5: (5, 7), (11, 13), (17, 19), (23, 29), (31, 37), (41, 43), (47, 53). Sequence gives differences between pairs. - Zak Seidov, Oct 05 2003

			a(4)=6 as a_o(5)=58 - a_e(5)=71 is 13 and a_o(4)=35 - a_e(4)=42 is 7 and the difference is 6.

Cf. A000040, A088680, A088682, A088683, A088684.

Table[ Prime[2n] - Prime[2n - 1], {n, 100}] (* Robert G. Wilson v, May 29 2004 *)

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar

A088680 a(n) = prime(2n+1) - prime(2n).

Original entry on oeis.org

2, 4, 4, 4, 2, 4, 4, 6, 6, 2, 4, 8, 2, 2, 14, 6, 10, 6, 4, 6, 10, 4, 12, 4, 4, 2, 6, 6, 6, 2, 14, 2, 14, 10, 4, 8, 6, 6, 4, 10, 10, 6, 6, 4, 4, 8, 8, 6, 2, 6, 6, 2, 10, 6, 6, 4, 12, 2, 6, 2, 4, 8, 8, 8, 6, 8, 4, 4, 10, 2, 2, 2, 14, 2, 14, 2, 20, 8, 8, 6, 14, 6, 8, 12, 6, 10, 6, 2, 2, 18, 2, 6, 8, 6, 2

Offset: 1

Zak Seidov, Oct 05 2003

Partition the primes into pairs starting with 3: (3, 5), (7, 11), (13, 17), (19, 23), (29, 31), (37, 41), (43, 47). Sequence gives differences between pairs.

A bisection of A001223.

Cf. A078584, A088682, A088683, A088684, A078584.

Table[Prime[2n + 1] - Prime[2n], {n, 100}] (* Robert G. Wilson v, May 29 2004 *)
Differences/@Partition[Prime[Range[2,200]],2]//Flatten (* Harvey P. Dale, Sep 22 2019 *)

a(n) = A001223(2*n).

Edited by Robert G. Wilson v, May 29 2004

Offset corrected. - R. J. Mathar, Feb 23 2017

A088684 Prime(3n+3)-prime(3n+1).

Original entry on oeis.org

6, 6, 8, 6, 8, 6, 10, 6, 6, 10, 12, 10, 8, 6, 24, 6, 12, 12, 10, 24, 6, 16, 10, 12, 14, 18, 12, 10, 6, 20, 12, 14, 16, 8, 16, 8, 6, 12, 12, 16, 18, 18, 10, 10, 18, 14, 6, 24, 6, 6, 24, 18, 12, 10, 14, 10, 12, 12, 8, 6, 12, 12, 12, 16, 20, 12, 18, 20, 8, 6, 14, 40, 26, 18, 10, 6, 22, 6

Offset: 1

Zak Seidov, Oct 05 2003

Minimal difference is 6 (for 3-tuplet). Repeating 6 means successive 3-tuplets.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A088680, A078584, A088682, A088683.

Primes:= select(isprime, [2,seq(i,i=3..10000)]):
seq(Primes[3*n+3]-Primes[3*n+1],n=1..(nops(Primes)-3)/3); # Robert Israel, Dec 15 2019

Last[#]-First[#]&/@Partition[Prime[Range[4,250]],3] (* Harvey P. Dale, Sep 06 2011 *)

Partition primes in triples starting with 7: {7, 11, 13}, {17, 19, 23}, {29, 31, 37}, {41, 43, 47}, {53, 59, 61}, {67, 71, 73}, {79, 83, 89}, {97, 101, 103}, {107, 109, 113}. Sequence gives differences between lesser and larger primes in triples.

A088682 a(n) = prime(3n+1) - prime(3n-1).

Original entry on oeis.org

4, 6, 10, 10, 10, 8, 8, 14, 6, 18, 8, 8, 10, 12, 6, 16, 10, 16, 8, 6, 18, 18, 12, 14, 10, 12, 12, 8, 14, 6, 12, 10, 20, 16, 8, 12, 12, 14, 6, 8, 10, 18, 14, 12, 12, 24, 12, 6, 18, 18, 6, 12, 12, 20, 12, 18, 8, 8, 12, 24, 6, 14, 28, 18, 12, 16, 8, 22, 6, 8, 6, 8, 12, 28, 6, 14, 8, 12, 6, 24

Offset: 1

Zak Seidov, Oct 05 2003

Previous name was: Partition the primes in triples starting with 3: {3, 5, 7}, {11, 13, 17}, {19, 23, 29}, {31, 37, 41}, {43, 47, 53}, {59, 61, 67}, {71, 73, 79}, {83, 89, 97}, {101, 103, 107}. Sequence gives differences between smallest and largest prime in each triple.

Minimal difference is 6 (for 3-tuplet) except first triple. Repeating 6 means successive 3-tuplets, see A088683, A088684, ...

Cf. A088680, A078584, A088683, A088684.

Table[Prime[3n+1]-Prime[3n-1],{n,80}] (* Harvey P. Dale, Jul 28 2020 *)

a(n) = prime(3*n+1) - prime(3*n-1); \\ Michel Marcus, Oct 05 2013

New name from Michel Marcus, Oct 05 2013

cp's OEIS Frontend

A078584 a(n) = prime(2n) - prime(2n-1).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A088680 a(n) = prime(2n+1) - prime(2n).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

A088684 Prime(3n+3)-prime(3n+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A088682 a(n) = prime(3*n+1) - prime(3*n-1).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Extensions

A088682 a(n) = prime(3n+1) - prime(3n-1).