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 1-7 of 7 results.

A088681 Duplicate of A078584.

Original entry on oeis.org

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
Offset: 0

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Author

Keywords

A094204 Duplicate of A078584.

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
Offset: 1

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Author

Keywords

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

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Author

Zak Seidov, Oct 05 2003

Keywords

Comments

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.

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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

Extensions

Edited by Robert G. Wilson v, May 29 2004
Offset corrected. - R. J. Mathar, Feb 23 2017

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

A177691 The odd values of PrimePi(.), with repetition.

Original entry on oeis.org

1, 3, 3, 5, 5, 7, 7, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 13, 13, 15, 15, 15, 15, 15, 15, 17, 17, 19, 19, 19, 19, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 27, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 31, 33, 33, 35, 35, 37, 37, 37, 37, 37, 37, 39, 39, 39
Offset: 1

Views

Author

Giovanni Teofilatto, May 11 2010

Keywords

Links

Crossrefs

Cf. A000720, A005408.

Programs

  • Maple
    seq((2*n-1)$(ithprime(2*n)-ithprime(2*n-1)),n=1..30); # Robert Israel, Feb 13 2019
  • Mathematica
    Select[PrimePi[Range[300]],OddQ] (* Harvey P. Dale, Dec 24 2014 *)

Formula

Obtained by removing all even numbers from A000720. Block lengths (frequencies of repetitions) are in A078584.

Extensions

Erroneous formula removed by R. J. Mathar, May 14 2010
Showing 1-7 of 7 results.

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