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.
%I A144562 #54 Nov 04 2024 15:05:34
%S A144562 3,6,11,9,16,23,12,21,30,39,15,26,37,48,59,18,31,44,57,70,83,21,36,51,
%T A144562 66,81,96,111,24,41,58,75,92,109,126,143,27,46,65,84,103,122,141,160,
%U A144562 179,30,51,72,93,114,135,156,177,198,219,33,56,79,102,125,148,171,194,217,240,263
%N A144562 Triangle read by rows: T(n, k) = 2*n*k + n + k - 1.
%C A144562 Rearrangement of A153238, numbers n such that 2*n+3 is not prime (we have 2*T(n,k) + 3 = (2*n+1)*(2*k+1), as 2*n+3 is odd it consists of (at least) two odd factors and all such factors appear by definition).
%H A144562 Vincenzo Librandi, <a href="/A144562/b144562.txt">Rows n = 1..100, flattened</a>
%H A144562 Mutsumi Suzuki <a href="http://mathforum.org/te/exchange/hosted/suzuki/Vincent.html">Vincenzo Librandi's method for sequential primes</a> (Librandi's description in Italian).
%F A144562 Sum_{k=1..n} T(n,k) = n*(2*n^2 + 5*n - 1)/2 = A144640(n). - _G. C. Greubel_, Mar 01 2021
%F A144562 G.f.: x*y*(3 + 2*x*y + 2*x^3*y^2 - x^2*y*(6 + y))/((1 - x)^2*(1 - x*y)^3). - _Stefano Spezia_, Nov 04 2024
%e A144562 Triangle begins:
%e A144562 3;
%e A144562 6, 11;
%e A144562 9, 16, 23;
%e A144562 12, 21, 30, 39;
%e A144562 15, 26, 37, 48, 59;
%e A144562 18, 31, 44, 57, 70, 83;
%e A144562 21, 36, 51, 66, 81, 96, 111;
%e A144562 24, 41, 58, 75, 92, 109, 126, 143;
%e A144562 27, 46, 65, 84, 103, 122, 141, 160, 179;
%e A144562 ...
%p A144562 A144562:= (n,k) -> 2*n*k +n +k -1; seq(seq(A144562(n,k), k=1..n), n=1..12); # _G. C. Greubel_, Mar 01 2021
%t A144562 T[n_, k_]:= 2*n*k +n +k -1; Table[T[n, k], {n, 11}, {k, n}]//Flatten
%o A144562 (Magma) [2*n*k+n+k-1: k in [1..n], n in [1..11]]; /* or, see example: */ [[2*n*k+n+k-1: k in [1..n]]: n in [1..9]]; // _Bruno Berselli_, Dec 04 2011
%o A144562 (PARI) T(n,k)=2*n*k+n+k-1 \\ _Charles R Greathouse IV_, Dec 28 2011
%o A144562 (Sage) flatten([[2*n*k+n+n-1 for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Mar 01 2021
%Y A144562 Cf. A067076, A144640, A153238.
%Y A144562 Main diagonal gives A142463.
%Y A144562 T(2n,n) gives A180863(n+1).
%K A144562 nonn,easy,tabl
%O A144562 1,1
%A A144562 _Vincenzo Librandi_, Jan 06 2009
%E A144562 Edited by _Ray Chandler_, Jan 07 2009