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A302445 Triangle read by rows: row n gives primes of form k^2 + n - k for 0 < k < n.

%I A302445 #50 Feb 16 2025 08:33:53
%S A302445 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 A302445 19,43,103,17,71,197,17,19,23,29,37,47,59,73,89,107,127,149,173,199,
%U A302445 227,257,19,31,61,109,151,229,23,41,131,293,401,23,29,43,53,79,113,179,233,263,443
%N A302445 Triangle read by rows: row n gives primes of form k^2 + n - k for 0 < k < n.
%H A302445 Seiichi Manyama, <a href="/A302445/b302445.txt">Rows n = 2..421, flattened</a>
%H A302445 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LuckyNumberofEuler.html">Lucky Number of Euler</a>
%H A302445 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%H A302445 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler">Lucky numbers of Euler</a>
%e A302445   n\k|  1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16
%e A302445   ---+-----------------------------------------------------------------------
%e A302445     2|  2;
%e A302445     3|  3,  5;
%e A302445     4|
%e A302445     5|  5,  7, 11, 17;
%e A302445     6|
%e A302445     7|  7,   , 13, 19,   , 37;
%e A302445     8|
%e A302445     9|   , 11,   ,   , 29,   ,   ,   ;
%e A302445    10|
%e A302445    11| 11, 13, 17, 23, 31, 41, 53, 67, 83, 101;
%e A302445    12|
%e A302445    13| 13,   , 19,   ,   , 43,   ,   ,   , 103,    ,    ;
%e A302445    14|
%e A302445    15|   , 17,   ,   ,   ,   ,   , 71,   ,    ,    ,    ,    , 197;
%e A302445    16|
%e A302445    17| 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257;
%t A302445 Map[Union@ Select[#, PrimeQ] &, Table[k^2 + n - k, {n, 23}, {k, 0, n}]] // Flatten (* _Michael De Vlieger_, Apr 10 2018 *)
%o A302445 (GAP) a:=Filtered(Flat(List([1..10],n->List([1..n],k->k^2+n-k))),IsPrime); # _Muniru A Asiru_, Apr 09 2018
%Y A302445 Row n: A027753 (n=3), A027755 (n=5), A048059 (n=11), A007635 (n=17), A005846 (n=41).
%Y A302445 Cf. A000040, A014556, A302826.
%K A302445 nonn,tabf
%O A302445 2,1
%A A302445 _Seiichi Manyama_, Apr 08 2018