A221491 Number of primes of the form k*n - k + n, 1 <= k <= n.

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

Offset

1,3

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

a[n_] := Sum[Boole[PrimeQ[(k+1)(n-1)+1]], {k, 1, n}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 20 2021 *)

Prog

(Haskell)
a221491 n = sum [a010051' (k*n - k + n) | k <- [1..n]]
(PARI) a(n) = sum(k=1, n, isprime(k*n - k + n)); \\ Michel Marcus, Jan 26 2022

Crossrefs

Cf. A221490.

Cf. A010051, A162610.

Sequence in context: A130325 A362034 A154097 * A224254 A107604 A080647

Adjacent sequences: A221488 A221489 A221490 * A221492 A221493 A221494

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jan 19 2013

Status

approved