cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Nov 30 2002

Keywords

Comments

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

Examples

			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.

Crossrefs

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

Programs

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

Extensions

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

A088683 a(n) = prime(3*n+2) - prime(3*n).

Original entry on oeis.org

6, 6, 8, 6, 12, 10, 10, 12, 6, 18, 12, 12, 12, 12, 14, 6, 8, 12, 8, 12, 6, 20, 6, 14, 10, 12, 12, 10, 12, 16, 12, 18, 24, 12, 16, 8, 10, 22, 10, 14, 14, 18, 12, 14, 12, 22, 12, 12, 6, 18, 24, 18, 10, 18, 14, 16, 12, 16, 12, 22, 10, 14, 24, 18, 14, 10, 8, 28, 10, 10, 16, 40, 14, 24, 6
Offset: 1

Views

Author

Zak Seidov, Oct 05 2003

Keywords

Comments

Previous name was: Differences in triples of primes.
Minimal difference is 6 (for 3-tuplet) except first triple. Repeating 6 means successive 3-tuplets, see A088683, A088684..

Links

Crossrefs

Cf. A088680, A078584, A088682, A088684.

Programs

  • Magma
    [NthPrime(3*n+2) - NthPrime(3*n): n in [1..80]]; // G. C. Greubel, May 19 2019
  • Mathematica
    #[[3]]-#[[1]]&/@Partition[Prime[Range[3,300]],3]  (* Harvey P. Dale, Jan 12 2011 *)
  • PARI
    a(n) = prime(3*n+2) - prime(3*n); \\ Michel Marcus, Oct 05 2013
  • Sage
    [nth_prime(3*n+2) - nth_prime(3*n) for n in (1..80)] # G. C. Greubel, May 19 2019

Formula

Partition primes in triples starting with 5: {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, 109}. Sequence gives differences between lesser and larger primes in triples.

Extensions

New name from Michel Marcus, Oct 05 2013

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

Views

Author

Zak Seidov, Oct 05 2003

Keywords

Comments

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

Links

Crossrefs

Cf. A088680, A078584, A088682, A088683.

Programs

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

Formula

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(3*n+1) - prime(3*n-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

Views

Author

Zak Seidov, Oct 05 2003

Keywords

Comments

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, ...

Crossrefs

Cf. A088680, A078584, A088683, A088684.

Programs

  • Mathematica
    Table[Prime[3n+1]-Prime[3n-1],{n,80}] (* Harvey P. Dale, Jul 28 2020 *)
  • PARI
    a(n) = prime(3*n+1) - prime(3*n-1); \\ Michel Marcus, Oct 05 2013

Extensions

New name from Michel Marcus, Oct 05 2013

A177692 The even values of PrimePi(.), with repetition.

Original entry on oeis.org

0, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 12, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 24, 24, 24, 24, 26, 26, 28, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32
Offset: 1

Views

Author

Giovanni Teofilatto, May 11 2010

Keywords

Crossrefs

Cf. A000720, A005843.

Formula

Obtained by removing all odd numbers from A000720. Block lengths (frequencies of repetitions) are in A088680.

Extensions

Erroneous formula removed by R. J. Mathar, May 14 2010
Showing 1-5 of 5 results.

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