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.

A155722 Numbers k such that 2*k + 9 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 10, 11, 14, 16, 17, 19, 22, 25, 26, 29, 31, 32, 35, 37, 40, 44, 46, 47, 49, 50, 52, 59, 61, 64, 65, 70, 71, 74, 77, 79, 82, 85, 86, 91, 92, 94, 95, 101, 107, 109, 110, 112, 115, 116, 121, 124, 127, 130, 131, 134, 136, 137, 142, 149, 151, 152, 154, 161, 164
Offset: 1

Views

Author

Vincenzo Librandi, Jan 25 2009

Keywords

Comments

Subsequence of A001651; A011655(a(n)) = 1. - Reinhard Zumkeller, Jul 09 2010
One less than the associated entry in A105760, two less than in A089038, three less than in A067076. - R. J. Mathar, Jan 05 2011

Crossrefs

Numbers h such that 2*h + k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), this seq (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).

Programs

Extensions

Edited by N. J. A. Sloane, Jun 23 2010
Definition clarified by Zak Seidov, Jul 11 2014

A155724 Triangle read by rows: T(n, k) = 2*n*k + n + k - 4.

Original entry on oeis.org

0, 3, 8, 6, 13, 20, 9, 18, 27, 36, 12, 23, 34, 45, 56, 15, 28, 41, 54, 67, 80, 18, 33, 48, 63, 78, 93, 108, 21, 38, 55, 72, 89, 106, 123, 140, 24, 43, 62, 81, 100, 119, 138, 157, 176, 27, 48, 69, 90, 111, 132, 153, 174, 195, 216, 30, 53, 76, 99, 122, 145, 168, 191, 214, 237, 260
Offset: 1

Views

Author

Vincenzo Librandi, Jan 25 2009

Keywords

Examples

			Triangle begins:
   0;
   3,  8;
   6, 13, 20;
   9, 18, 27, 36;
  12, 23, 34, 45,  56;
  15, 28, 41, 54,  67,  80;
  18, 33, 48, 63,  78,  93, 108;
  21, 38, 55, 72,  89, 106, 123, 140;
  24, 43, 62, 81, 100, 119, 138, 157, 176;
  27, 48, 69, 90, 111, 132, 153, 174, 195, 216;
		

Crossrefs

All terms are in A155723.
Cf. A162261 (row sums).
Columns k: A008585 (k=1), A016885 (k=2), A017053 (k=3), 9*A020705 (k=4).
Diagonals include: A139570, A181510, A271625.

Programs

  • Magma
    /* Triangle: */ [[2*m*n+m+n-4: m in [1..n]]: n in [1..10]]; // Bruno Berselli, Aug 31 2012
    
  • Mathematica
    Flatten[Table[2 n m + m + n - 4, {n, 10}, {m, n}]] (* Vincenzo Librandi, Mar 01 2012 *)
  • Python
    def A155724(n,k): return 2*n*k+n+k-4
    print(flatten([[A155724(n,k) for k in range(1,n+1)] for n in range(1,16)])) # G. C. Greubel, Jan 21 2025

Formula

T(n, k) = A154685(n, k) - 8. - L. Edson Jeffery, Oct 12 2012
2*T(n, k) + 9 = (2*k+1)*(2*n+1). - Vincenzo Librandi, Nov 18 2012
From G. C. Greubel, Jan 21 2025: (Start)
T(2*n-1, n) = 4*n^2 + n - 5 (main diagonal).
Sum_{k=1..n} (-1)^(k-1)*T(n, k) = (1/4)*( 4*(-1)^(n+1)*n^2 + 2*(2-3*(-1)^n)*n - 7*(1-(-1)^n)).
G.f.: x*y*(3*x + 3*y - 4*x*y)/((1-x)*(1-y))^2. (End)

Extensions

Edited by N. J. A. Sloane, Jun 23 2010

A153083 Numbers such that 2*n + 11 is not prime.

Original entry on oeis.org

2, 5, 7, 8, 11, 12, 14, 17, 19, 20, 22, 23, 26, 27, 29, 32, 33, 35, 37, 38, 40, 41, 42, 44, 47, 50, 52, 53, 54, 55, 56, 57, 59, 61, 62, 65, 66, 67, 68, 71, 72, 74, 75, 77, 79, 80, 82, 83, 86, 87, 88, 89, 92, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 107, 110, 112
Offset: 1

Views

Author

Vincenzo Librandi, Dec 18 2008

Keywords

Comments

One less than the associated entry in A155723. [ R. J. Mathar, Jan 05 2011]

Examples

			Distribution of the terms in the following triangular array:
*
2,7;
5,12,19;
8,17,26,35;
11,22,33,44,55;
14,27,40,53,66,79;
17,32,47,62,77,92,107;
20,37,54,71,88,105,122,139;
23,42,61,80,99,118,137,156,175;
26,47,68,89,110,131,152,173,194,215;
29,52,75,98,121,144,167,190,213,236,259;
32,57,82,107,132,157,182,207,232,257,282,307;
where * marks the decimal values of (2*h*k + k + h - 5) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013
		

Crossrefs

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 11)]; // Vincenzo Librandi, Nov 21 2012
  • Mathematica
    Select[Range[100],!PrimeQ[2#+11]&] (* Harvey P. Dale, Jul 18 2011 *)
Showing 1-3 of 3 results.