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 1-3 of 3 results.

A153144 Numbers n such that 2*n+19 is not a prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 10, 13, 15, 16, 18, 19, 22, 23, 25, 28, 29, 31, 33, 34, 36, 37, 38, 40, 43, 46, 48, 49, 50, 51, 52, 53, 55, 57, 58, 61, 62, 63, 64, 67, 68, 70, 71, 73, 75, 76, 78, 79, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101
Offset: 1

Views

Author

Vincenzo Librandi, Dec 19 2008

Keywords

Links

Crossrefs

Cf. A153143, A153081, A155551.
Numbers n such that 2n+k is not prime: A047845 (k=1), A153238 (k=3), A153052 (k=5), A153053 (k=7), A153723 (k=9), A153083 (k=11), A153082 (k=13), A241571 (k=15), A241572 (k=17), this sequence (k=19).

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 19)]; // Vincenzo Librandi, Dec 13 2012
  • Mathematica
    Select[Range[0, 500], !PrimeQ[2# + 19] &] (* Vincenzo Librandi, Dec 13 2012 *)

A162259 a(n) = (2*n^3 + 5*n^2 - 17*n)/2.

Original entry on oeis.org

-5, 1, 24, 70, 145, 255, 406, 604, 855, 1165, 1540, 1986, 2509, 3115, 3810, 4600, 5491, 6489, 7600, 8830, 10185, 11671, 13294, 15060, 16975, 19045, 21276, 23674, 26245, 28995, 31930, 35056, 38379, 41905, 45640, 49590, 53761, 58159, 62790, 67660
Offset: 1

Views

Author

Vincenzo Librandi, Jun 29 2009

Keywords

Links

Crossrefs

Cf. A155551.

Programs

  • Mathematica
    CoefficientList[Series[(-5+21*x-10*x^2)/(1-x)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {-5, 1, 24, 70}, 50] (* Vincenzo Librandi, Mar 04 2012 *)
Table[(2n^3+5n^2-17n)/2,{n,40}] (* Harvey P. Dale, May 10 2021 *)

Formula

Row sums from A155551: a(n) = Sum_{m=1..n} (2*m*n + m + n - 9).
From Vincenzo Librandi, Mar 04 2012: (Start)
G.f.: x*(-5 + 21*x - 10*x^2)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Extensions

New name from Vincenzo Librandi, Mar 04 2012

A324937 Triangle read by rows: T(n, k) = 2*n*k + n + k - 8.

Original entry on oeis.org

-4, -1, 4, 2, 9, 16, 5, 14, 23, 32, 8, 19, 30, 41, 52, 11, 24, 37, 50, 63, 76, 14, 29, 44, 59, 74, 89, 104, 17, 34, 51, 68, 85, 102, 119, 136, 20, 39, 58, 77, 96, 115, 134, 153, 172, 23, 44, 65, 86, 107, 128, 149, 170, 191, 212, 26, 49, 72, 95, 118, 141, 164, 187, 210, 233, 256
Offset: 1

Views

Author

Vincenzo Librandi, Mar 25 2019

Keywords

Examples

			Triangle begins:
  -4;
  -1, 4;
   2, 9,  16;
   5, 14, 23, 32;
   8, 19, 30, 41, 52;
  11, 24, 37, 50, 63, 76;
  14, 29, 44, 59, 74, 89,  104;
  17, 34, 51, 68, 85, 102, 119, 136;
  20, 39, 58, 77, 96, 115, 134, 153, 172;  etc.

Crossrefs

Similar sequence T(n,k) = 2*n*k+n+k-h: A144562 (h=1); A154680 (h=2); A154684 (h=3); A155724 (h=4); A155546 (h=5); A155550 (h=6); A144670 (h=7); this sequence (h=8); A155551 (h=9).

Programs

  • Magma
    [2*n*k+n+k-8: k in [1..n], n in [1..11]]; /* As triangle */ [[2*n*k+n+k-8: k in [1..n]]: n in [1.. 15]];
  • Mathematica
    t[n_, k_]:=2 n k + n + k - 8; Table[t[n, k], {n, 11}, {k, n}]//Flatten

Formula

G.f.: x*y*(9*x^3*y^2 - 4*x^2*y*(5 + 2*y) + x*(7 + 16*y) - 4)/((1 - x)^2*(1 - x*y)^3). - Stefano Spezia, Jul 29 2025
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.