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 1-6 of 6 results.

A126993 a(n) = binomial(prime(n+3), prime(n)).

Original entry on oeis.org

21, 165, 1287, 19448, 75582, 1144066, 51895935, 141120525, 6107086800, 7898654920, 15338678264, 5178066751, 266783135710, 109712808959985, 22512762077400, 97862516286480, 12802736917880, 18385569737808
Offset: 1

Views

Author

Artur Jasinski, Jan 01 2007

Keywords

Crossrefs

Programs

  • Magma
    [Binomial(NthPrime(n+3), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019
    
  • Mathematica
    Table[Binomial[Prime[n+3], Prime[n]], {x, 1, 20}]
  • PARI
    vector(20, n, binomial(prime(n+3), prime(n))) \\ G. C. Greubel, May 29 2019
    
  • Sage
    [binomial(nth_prime(n+3), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019

A126996 a(n) = binomial(prime(3+n), prime(3)).

Original entry on oeis.org

1, 21, 462, 1287, 6188, 11628, 33649, 118755, 169911, 435897, 749398, 962598, 1533939, 2869685, 5006386, 5949147, 9657648, 13019909, 15020334, 22537515, 29034396, 41507642, 64446024, 79208745, 87541245, 106308566, 116828271, 140364532, 254231775
Offset: 0

Views

Author

Artur Jasinski, Jan 01 2007

Keywords

Crossrefs

Programs

  • Magma
    [Binomial(NthPrime(n+3), 5): n in [0..30]]; // Vincenzo Librandi, May 21 2019
    
  • Mathematica
    Table[Binomial[Prime[n + 3], Prime[3]], {n, 0, 30}]
    Binomial[Prime[Range[3,40]],5] (* Harvey P. Dale, Mar 20 2021 *)
  • PARI
    vector(30, n, binomial(prime(n+3), 5)) \\ G. C. Greubel, May 29 2019
    
  • Sage
    [binomial(nth_prime(n+3), 5) for n in (1..30)] # G. C. Greubel, May 29 2019

Extensions

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126997 a(n) = binomial(prime(4+n), prime(4)).

Original entry on oeis.org

1, 330, 1716, 19448, 50388, 245157, 1560780, 2629575, 10295472, 22481940, 32224114, 62891499, 154143080, 341149446, 436270780, 869648208, 1329890705, 1629348612, 2898753715, 4151918628, 6890268572, 12846240784, 17199613200, 19813501785, 26075972546, 29796772356, 38620298376
Offset: 0

Views

Author

Artur Jasinski, Jan 01 2007

Keywords

Crossrefs

Programs

  • Magma
    [Binomial(NthPrime(n+4), 7): n in [1..30]]; // Vincenzo Librandi, May 21 2019
    
  • Mathematica
    Table[Binomial[Prime[n + 4], Prime[4]], {n, 1, 30}]
  • PARI
    vector(30, n, binomial(prime(n+4), prime(4)) ) \\ G. C. Greubel, May 29 2019
    
  • Sage
    [binomial(nth_prime(n+4), 7) for n in (1..30)] # G. C. Greubel, May 29 2019

Extensions

Terms a(24) onward added by G. C. Greubel, May 30 2019
Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126998 a(n) = binomial(prime(n+5), prime(5)).

Original entry on oeis.org

1, 78, 12376, 75582, 1352078, 34597290, 84672315, 854992152, 3159461968, 5752004349, 17417133617, 76223753060, 279871768995, 418094152866, 1285063345176, 2560547383576, 3558497368608, 9036996468045, 16141841823510, 36519676207704, 99468442390512, 158940114100040
Offset: 0

Views

Author

Artur Jasinski, Jan 01 2007

Keywords

Crossrefs

Programs

  • Magma
    [Binomial(NthPrime(n+5), NthPrime(5)): n in [1..30]]; // G. C. Greubel, May 29 2019
    
  • Mathematica
    Table[Binomial[Prime[n+5], Prime[5]], {n, 1, 30}]
  • PARI
    vector(30, n, binomial(prime(n+5), prime(5)) ) \\ G. C. Greubel, May 29 2019
    
  • Sage
    [binomial(nth_prime(n+5), nth_prime(5)) for n in (1..30)] # G. C. Greubel, May 29 2019

Extensions

Terms a(19) onward added by G. C. Greubel, May 30 2019
Missing n=0 term added by N. J. A. Sloane, May 17 2020

A126994 a(n) = binomial(prime(n+5), prime(n)).

Original entry on oeis.org

1, 78, 680, 11628, 245157, 34597290, 206253075, 15905368710, 244662670200, 960566918220, 4568648125690, 462525733568080, 8964377427999630, 6236646703759395, 972963730453314600, 5300174441392685400
Offset: 0

Views

Author

Artur Jasinski, Jan 01 2007

Keywords

Crossrefs

Programs

  • Magma
    [Binomial(NthPrime(n+5), NthPrime(n)): n in [1..20]]; // G. C. Greubel, May 29 2019
    
  • Mathematica
    Table[Binomial[Prime[n+5], Prime[n]], {n, 0, 20}]
  • PARI
    vector(20, n, binomial(prime(n+5), prime(n))) \\ G. C. Greubel, May 29 2019
    
  • Sage
    [binomial(nth_prime(n+5), nth_prime(n)) for n in (1..20)] # G. C. Greubel, May 29 2019

Extensions

Missing n=0 term added by N. J. A. Sloane, May 17 2020

A262248 Number of intersections of diagonals in the interior of a regular p-gon where p is the n-th prime.

Original entry on oeis.org

0, 0, 5, 35, 330, 715, 2380, 3876, 8855, 23751, 31465, 66045, 101270, 123410, 178365, 292825, 455126, 521855, 766480, 971635, 1088430, 1502501, 1837620, 2441626, 3464840, 4082925, 4421275, 5160610, 5563251, 6438740, 10334625, 11716640, 14043870
Offset: 1

Views

Author

Altug Alkan, Sep 16 2015

Keywords

Comments

This is binomial(prime(n),4). - N. J. A. Sloane, May 17 2020
Subsequence of A006561.
a(n) = prime(n) only for n = 3.

Examples

			For prime(2)=3, there is no intersection of diagonals in the interior of a regular triangle, so a(2)=0.
		

Crossrefs

Programs

  • Magma
    [(NthPrime(n)^4-6*(NthPrime(n)^3)+11*NthPrime(n)^2- 6*NthPrime(n))/24: n in [1..40]]; // Vincenzo Librandi, Sep 17 2015
  • Mathematica
    Table[(Prime[n]^4 - 6 (Prime[n]^3) + 11 Prime[n]^2 - 6 Prime[n])/24, {n, 50}] (* Vincenzo Librandi, Sep 17 2015 *)
    (#^4-6#^3+11#^2-6#)/24&/@Prime[Range[40]] (* Harvey P. Dale, Jun 17 2022 *)
  • PARI
    a(n) = my(p=prime(n)); p*(p^3 - 6*p^2 + 11*p - 6)/24;
    vector(40, n, a(n))
    

Formula

a(n) = (prime(n)^4 - 6*prime(n)^3 + 11*prime(n)^2 - 6*prime(n))/24.
a(n) = A006561(A000040(n)).
Showing 1-6 of 6 results.