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.

A153082 Numbers k such that 2*k + 13 is not prime.

Original entry on oeis.org

1, 4, 6, 7, 10, 11, 13, 16, 18, 19, 21, 22, 25, 26, 28, 31, 32, 34, 36, 37, 39, 40, 41, 43, 46, 49, 51, 52, 53, 54, 55, 56, 58, 60, 61, 64, 65, 66, 67, 70, 71, 73, 74, 76, 78, 79, 81, 82, 85, 86, 87, 88, 91, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 106, 109, 111
Offset: 1

Views

Author

Vincenzo Librandi, Dec 18 2008

Keywords

Comments

One less than the associated entry in A153083. - R. J. Mathar, Jan 05 2011

Examples

			Distribution in the following triangular array:
*;
1, 6;
4, 11,18;
7, 16,25,34;
10,21,32,43,54;
13,26,39,52,65,78;
16,31,46,61,76,91,106;
19,36,53,70,87,104,121,138;
22,41,60,79,98,117,136,155,174;
25,46,67,88,109,130,151,172,193,214;
28,51,74,97,120,143,166,189,212,235,258;
31,56,81,106,131,156,181,206,231,256,281,306;
34,61,88,115,142,169,196,223,250,277,304,331,358; etc.
where * marks the negative values of (2*h*k + k + h - 6) with h >= k >= 1. -
_Vincenzo Librandi_, Jan 15 2013
		

Crossrefs

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 13)]; // Vincenzo Librandi, Nov 21 2012
  • Mathematica
    Select[Range[0,100],!PrimeQ[2#+13]&]  (* Harvey P. Dale, Mar 17 2011 *)

A162257 a(n) = (2*n^3 + 5*n^2 - 11*n)/2.

Original entry on oeis.org

-2, 7, 33, 82, 160, 273, 427, 628, 882, 1195, 1573, 2022, 2548, 3157, 3855, 4648, 5542, 6543, 7657, 8890, 10248, 11737, 13363, 15132, 17050, 19123, 21357, 23758, 26332, 29085, 32023, 35152, 38478, 42007, 45745, 49698, 53872, 58273, 62907, 67780
Offset: 1

Views

Author

Vincenzo Librandi, Jun 29 2009

Keywords

Crossrefs

Cf. A155550.

Programs

  • Maple
    A162257:=n->(2*n^3+5*n^2-11*n)/2: seq(A162257(n), n=1..80); # Wesley Ivan Hurt, Jan 30 2017
  • Mathematica
    CoefficientList[Series[(-2+15*x-7*x^2)/(1-x)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {-2, 7, 33, 82}, 50] (* Vincenzo Librandi, Mar 04 2012 *)

Formula

Row sums from A155550: a(n) = Sum_{m=1..n} 2*m*n + m + n - 6.
From Vincenzo Librandi, Mar 04 2012: (Start)
G.f.: x*(-2 + 15*x - 7*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.