A163676 - OEIS

%I #17 Sep 08 2022 08:45:47

%S 7,13,23,19,33,47,25,43,61,79,31,53,75,97,119,37,63,89,115,141,167,43,

%T 73,103,133,163,193,223,49,83,117,151,185,219,253,287,55,93,131,169,

%U 207,245,283,321,359,61,103,145,187,229,271,313,355,397,439,67,113,159

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

%C 2 + T(n,m) = (2*n+1)*(2*m+1) are composite numbers. - clarified by _R. J. Mathar_, Oct 16 2009

%C First column: A016921, second column: A017305, third column: A126980. - _Vincenzo Librandi_, Nov 21 2012

%H Vincenzo Librandi, <a href="/A163676/b163676.txt">Rows n = 1..100, flattened</a>

%F T(n,m) = A155151(n,m) - 3 = A155156(n,m) - 1. - _R. J. Mathar_, Oct 16 2009

%e Triangle begins:

%e    7;

%e   13,  23;

%e   19,  33,  47;

%e   25,  43,  61,  79;

%e   31,  53,  75,  97, 119;

%e   37,  63,  89, 115, 141, 167;

%e   43,  73, 103, 133, 163, 193, 223;

%e   49,  83, 117, 151, 185, 219, 253, 287;

%e   55,  93, 131, 169, 207, 245, 283, 321, 359;

%e   61, 103, 145, 187, 229, 271, 313, 355, 397, 439;

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

%o (Magma) [4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 21 2012

%o (PARI) for(n=1,10, for(k=1,n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ _G. C. Greubel_, Aug 02 2017

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

%K nonn,easy,tabl

%O 1,1

%A _Vincenzo Librandi_, Aug 03 2009