A350377 Numbers k such that Sum_{j=1..k} (pi(k*j-j+1) - pi(k*j-j)) = Sum_{i=1..k} (pi(k*(i-1)+i) - pi(k*(i-1)+i-1)).

1, 5, 8, 10, 11, 12, 14, 21, 23, 24, 27, 63, 64, 72, 90, 99, 144, 176, 184, 340, 366, 393, 480, 567, 693, 915, 975, 1046, 1068, 1084, 1260, 1410, 1452, 1830, 1968, 2268, 2490, 2943, 3087, 3735, 5284, 5426, 5637, 5757, 6015, 6334, 6393, 6570, 6582, 8292, 9836, 10005

Offset

1,2

Comments

Numbers with the same number of primes appearing along the main diagonal and along the main antidiagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see example).

Links

Table of n, a(n) for n=1..52.

Formula

Numbers k such that A221490(k) = A344349(k).

Example

5 is in the sequence since there are 3 primes along the main diagonal and 3 primes along the main antidiagonal of the 5 X 5 array below.
  [1   2  3  4  5]
  [6   7  8  9 10]
  [11 12 13 14 15]
  [16 17 18 19 20]
  [21 22 23 24 25]

Mathematica

q[k_] := Sum[Boole @ PrimeQ[k*j - j + 1] - Boole @ PrimeQ[k*(j - 1) + j], {j, 1, k}] == 0; Select[Range[1000], q] (* Amiram Eldar, Dec 28 2021 *)

Crossrefs

Cf. A000720 (pi), A221490, A344349, A350328.

Sequence in context: A006186 A230457 A180748 * A121901 A024707 A156288

Adjacent sequences: A350374 A350375 A350376 * A350378 A350379 A350380

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 28 2021

Extensions

More terms from Amiram Eldar, Dec 28 2021

Status

approved