A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

7, 13, 23, 19, 33, 47, 25, 43, 61, 79, 31, 53, 75, 97, 119, 37, 63, 89, 115, 141, 167, 43, 73, 103, 133, 163, 193, 223, 49, 83, 117, 151, 185, 219, 253, 287, 55, 93, 131, 169, 207, 245, 283, 321, 359, 61, 103, 145, 187, 229, 271, 313, 355, 397, 439, 67, 113, 159

Offset: 1

Author

Vincenzo Librandi, Aug 03 2009

Keywords

• nonn
• easy
• tabl

Comments

2 + T(n,m) = (2*n+1)*(2*m+1) are composite numbers. - clarified by R. J. Mathar, Oct 16 2009

First column: A016921, second column: A017305, third column: A126980. - Vincenzo Librandi, Nov 21 2012

Examples

			Triangle begins:
   7;
  13,  23;
  19,  33,  47;
  25,  43,  61,  79;
  31,  53,  75,  97, 119;
  37,  63,  89, 115, 141, 167;
  43,  73, 103, 133, 163, 193, 223;
  49,  83, 117, 151, 185, 219, 253, 287;
  55,  93, 131, 169, 207, 245, 283, 321, 359;
  61, 103, 145, 187, 229, 271, 313, 355, 397, 439;
		

Links

• Vincenzo Librandi, Rows n = 1..100, flattened

Crossrefs

Cf. A016921, A017305, A126980, A155151, A155156.

Programs

Magma

[4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012

Mathematica

t[n_,k_]:=4 n*k + 2n + 2k - 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)

PARI

for(n=1,10, for(k=1,n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ G. C. Greubel, Aug 02 2017

Formula

T(n,m) = A155151(n,m) - 3 = A155156(n,m) - 1. - R. J. Mathar, Oct 16 2009