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A140869 Triangle read by rows where T(m,n) = floor((2mn+m+n-2)/2), m >= n >= 1.

%I A140869 #22 Sep 08 2022 08:45:35
%S A140869 1,2,5,4,7,11,5,10,14,19,7,12,18,23,29,8,15,21,28,34,41,10,17,25,32,
%T A140869 40,47,55,11,20,28,37,45,54,62,71,13,22,32,41,51,60,70,79,89,14,25,35,
%U A140869 46,56,67,77,88,98,109,16,27,39,50,62,73,85,96,108,119,131,17,30,42,55,67,80,92,105,117,130,142,155
%N A140869 Triangle read by rows where T(m,n) = floor((2mn+m+n-2)/2), m >= n >= 1.
%C A140869 Conjecture: If h does not belong to the sequence, then 4*h+5 is prime. - _Vincenzo Librandi_, Nov 18 2012
%C A140869 First column: A001651; second column: A047215; third column: A047345. - _Vincenzo Librandi_, Nov 18 2012
%H A140869 Vincenzo Librandi, <a href="/A140869/b140869.txt">Rows n = 1..100, flattened</a>
%e A140869 Triangle begins:
%e A140869 1;
%e A140869 2,  5;
%e A140869 4,  7,  11;
%e A140869 5,  10, 14, 19;
%e A140869 7,  12, 18, 23, 29;
%e A140869 8,  15, 21, 28, 34, 41;
%e A140869 10, 17, 25, 32, 40, 47, 55; etc.
%t A140869 Flatten[Table[Floor[(2*n*m+m+n-2)/2],{n,1,10},{m,n}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012 *)
%o A140869 (Magma) [Floor(((2*n*k+n+k-2)/2)): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 18 2012
%Y A140869 Cf. A002327, A153085, A001651, A047215, A047345.
%K A140869 nonn,tabl,easy
%O A140869 1,2
%A A140869 _Vincenzo Librandi_, Jan 16 2009