A144652 - OEIS

%I #22 Sep 08 2022 08:45:38

%S 2,3,6,5,8,12,6,11,15,20,8,13,19,24,30,9,16,22,29,35,42,11,18,26,33,

%T 41,48,56,12,21,29,38,46,55,63,72,14,23,33,42,52,61,71,80,90,15,26,36,

%U 47,57,68,78,89,99,110,17,28,40,51,63,74,86,97,109,120,132,18,31,43,56,68

%N Triangle, read by rows, where T(m,n) = floor((2mn+m+n)/2) with m >= n >= 1.

%C From _Vincenzo Librandi_, Nov 16 2012: (Start)

%C First column:  A007494(n+1);

%C second column: A047219(n+2);

%C third column:  A047383(n+3);

%C fourth column: A193910(n+4).

%C Conjecture: If h does not belong to the sequence, then 4*h+1 is prime. (End)

%H Vincenzo Librandi, <a href="/A144652/b144652.txt">Rows n = 1..100, flattened</a>

%e Triangle begins:

%e 2;

%e 3,  6;

%e 5,  8,  12;

%e 6,  11, 15, 20;

%e 8,  13, 19, 24, 30;

%e 9,  16, 22, 29, 35, 42;

%e 11, 18, 26, 33, 41, 48, 56; etc.

%t Flatten[Table[Floor[(2*n*m + m + n)/2], {n, 1, 20}, {m, n}]] (* _Vincenzo Librandi_, Nov 16 2012 *)

%o (Magma) [Floor((2*n*k+n+k)/2): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 16 2012

%Y Cf. A007494, A047219, A047383, A193910.

%K nonn,tabl,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 27 2009

%E Definition edited (specifying m >= n >= 1), and terms recomputed to match definition, as was done with the similar sequence A140869, by _Jon E. Schoenfield_, Jun 24 2010