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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.
4
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
1,2
FORMULA
a(n) = Sum_{k=1..n} c(n*k-k+1), where c is the prime characteristic.
EXAMPLE
[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}
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MATHEMATICA
Table[Sum[PrimePi[n*k - k + 1] - PrimePi[n*k - k], {k, n}], {n, 100}]
CROSSREFS
Cf. A010051, A221490, A344316 (primes along border).
Sequence in context: A086489 A015886 A255354 * A318620 A287748 A260233
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 15 2021
STATUS
approved