A344349 Number of primes along the main antidiagonal of the n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.

0, 2, 3, 2, 3, 2, 6, 2, 3, 3, 6, 3, 7, 4, 7, 6, 6, 4, 10, 2, 8, 7, 9, 4, 11, 5, 10, 8, 11, 4, 17, 3, 10, 10, 12, 9, 16, 4, 10, 11, 14, 6, 21, 7, 11, 10, 16, 8, 19, 6, 19, 13, 17, 5, 25, 10, 19, 10, 16, 9, 27, 7, 16, 13, 16, 13, 31, 9, 18, 14, 27, 10, 26, 10, 20, 19, 17, 12, 30

Offset: 1

Author

Wesley Ivan Hurt, May 15 2021

Keywords

• nonn

Examples

			                                                      [1   2  3  4  5]
                                      [1   2  3  4]   [6   7  8  9 10]
                            [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
                   [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
           [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
------------------------------------------------------------------------
  n         1        2         3            4                 5
------------------------------------------------------------------------
  a(n)      0        2         3            2                 3
------------------------------------------------------------------------
  primes   {}      {2,3}    {3,5,7}       {7,13}          {5,13,17}
------------------------------------------------------------------------
		

Crossrefs

Cf. A010051, A221490, A344316 (primes along border).

Programs

Mathematica

Table[Sum[PrimePi[n*k - k + 1] - PrimePi[n*k - k], {k, n}], {n, 100}]

Formula

a(n) = Sum_{k=1..n} c(n*k-k+1), where c is the prime characteristic.