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%I #19 Jan 26 2022 14:20:43
%S 0,0,1,1,3,1,2,2,5,3,6,3,5,4,4,3,9,2,6,5,8,4,9,4,9,7,10,4,17,3,10,9,
%T 11,9,15,4,9,10,13,5,20,7,11,10,16,8,19,6,18,12,17,5,23,9,18,9,15,8,
%U 26,7,15,12,16,13,29,8,18,13,26,9,25,10,19,18,16
%N Number of primes of the form k*n + k - n, 1 <= k <= n.
%C Number of primes in n-th row of the triangle in A209297.
%C Number of primes along the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see square arrays in example). - _Wesley Ivan Hurt_, May 15 2021
%H Reinhard Zumkeller, <a href="/A221490/b221490.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{k=1..n} A010051(A209297(n,k)).
%F a(n) = Sum_{k=1..n} c(n*(k-1)+k), where c is the prime characteristic. - _Wesley Ivan Hurt_, May 15 2021
%e Row 10 of A209297 = [1,12,23,34,45,56,67,78,89,100] containing three primes: [23,67,89], therefore a(10) = 3;
%e row 11 of A209297 = [1,13,25,37,49,61,73,85,97,109,121] containing six primes: [13,37,61,73,97,109], therefore a(11) = 6.
%e From _Wesley Ivan Hurt_, May 15 2021: (Start)
%e [1 2 3 4 5]
%e [1 2 3 4] [6 7 8 9 10]
%e [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e ------------------------------------------------------------------------
%e n 1 2 3 4 5
%e ------------------------------------------------------------------------
%e a(n) 0 0 1 1 3
%e ------------------------------------------------------------------------
%e (End)
%t Count[#,_?PrimeQ]&/@Table[k*n+k-n,{n,75},{k,n}] (* _Harvey P. Dale_, Apr 03 2015 *)
%o (Haskell)
%o a221490 n = sum [a010051 (k*n + k - n) | k <- [1..n]]
%o (PARI) a(n) = sum(k=1, n, isprime(k*n + k - n)); \\ _Michel Marcus_, Jan 26 2022
%Y Cf. A010051, A209297, A221491, A344316, A344349.
%K nonn
%O 1,5
%A _Reinhard Zumkeller_, Jan 19 2013