A344349 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..79.

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}

------------------------------------------------------------------------

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

Adjacent sequences: A344346 A344347 A344348 * A344350 A344351 A344352

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2021

STATUS

approved