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Number of primes of the form k*n - k + n, 1 <= k <= n.
3

%I #13 Jan 26 2022 12:00:16

%S 0,1,2,2,2,2,5,2,3,3,5,3,6,4,7,6,5,4,9,2,8,7,8,4,11,5,10,8,10,4,16,3,

%T 10,10,12,9,15,4,10,11,13,6,20,7,11,10,15,8,19,6,19,13,16,5,25,10,19,

%U 10,15,9,26,7,16,13,16,13,30,9,18,14,26,10,25,10

%N Number of primes of the form k*n - k + n, 1 <= k <= n.

%C a(n) = sum(A010051(A162610(n,k)): k=1..n) = number of primes in n-th row of the triangle in A162610. - _Reinhard Zumkeller_, Jan 19 2013

%H Reinhard Zumkeller, <a href="/A221491/b221491.txt">Table of n, a(n) for n = 1..1000</a>

%e Row 10 of A162610 = [19,28,37,46,55,64,73,82,91,100] containing three primes: [19,37,73], therefore a(10) = 3;

%e row 11 of A162610 = [21,31,41,51,61,71,81,91,101,111,121] containing five primes: [31,41,61,71,101], therefore a(11) = 5.

%t a[n_] := Sum[Boole[PrimeQ[(k+1)(n-1)+1]], {k, 1, n}];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Sep 20 2021 *)

%o (Haskell)

%o a221491 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. A221490.

%Y Cf. A010051, A162610.

%K nonn,tabl

%O 1,3

%A _Reinhard Zumkeller_, Jan 19 2013