A344316 Number of primes appearing along the border of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
0, 2, 3, 4, 5, 7, 7, 8, 8, 10, 9, 13, 12, 13, 12, 12, 13, 20, 14, 17, 17, 19, 16, 22, 18, 22, 19, 23, 19, 31, 18, 26, 24, 26, 25, 31, 18, 27, 28, 30, 22, 39, 25, 30, 31, 37, 26, 41, 29, 37, 32, 42, 28, 44, 31, 39, 30, 41, 32, 51, 33, 39, 40, 41, 36, 52, 35, 44, 39, 50, 39, 52, 39
Offset: 1
Keywords
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 4 5
------------------------------------------------------------------------
primes {} {2,3} {2,3,7} {2,3,5,13} {2,3,5,11,23}
------------------------------------------------------------------------
Programs
-
Mathematica
Table[PrimePi[n] + PrimePi[n^2 - 1] - PrimePi[n*(n - 1)] + Sum[PrimePi[n*k + 1] - PrimePi[n*k], {k, n - 2}], {n, 100}]
Formula
a(n) = pi(n) + pi(n^2-1) - pi(n^2-n) + Sum_{k=1..n-2} (pi(n*k+1) - pi(n*k)).