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%I #49 May 23 2018 10:03:31
%S 2,3,5,5,7,11,17,7,13,19,37,11,29,11,13,17,23,31,41,53,67,83,101,13,
%T 19,43,103,17,71,197,17,19,23,29,37,47,59,73,89,107,127,149,173,199,
%U 227,257,19,31,61,109,151,229,23,41,131,293,401,23,29,43,53,79,113,179,233,263,443
%N Triangle read by rows: row n gives primes of form k^2 + n - k for 0 < k < n.
%H Seiichi Manyama, <a href="/A302445/b302445.txt">Rows n = 2..421, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LuckyNumberofEuler.html">Lucky Number of Euler</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler">Lucky numbers of Euler</a>
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
%e ---+-----------------------------------------------------------------------
%e 2| 2;
%e 3| 3, 5;
%e 4|
%e 5| 5, 7, 11, 17;
%e 6|
%e 7| 7, , 13, 19, , 37;
%e 8|
%e 9| , 11, , , 29, , , ;
%e 10|
%e 11| 11, 13, 17, 23, 31, 41, 53, 67, 83, 101;
%e 12|
%e 13| 13, , 19, , , 43, , , , 103, , ;
%e 14|
%e 15| , 17, , , , , , 71, , , , , , 197;
%e 16|
%e 17| 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257;
%t Map[Union@ Select[#, PrimeQ] &, Table[k^2 + n - k, {n, 23}, {k, 0, n}]] // Flatten (* _Michael De Vlieger_, Apr 10 2018 *)
%o (GAP) a:=Filtered(Flat(List([1..10],n->List([1..n],k->k^2+n-k))),IsPrime); # _Muniru A Asiru_, Apr 09 2018
%Y Row n: A027753 (n=3), A027755 (n=5), A048059 (n=11), A007635 (n=17), A005846 (n=41).
%Y Cf. A000040, A014556, A302826.
%K nonn,tabf
%O 2,1
%A _Seiichi Manyama_, Apr 08 2018
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