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%I A350377 #8 Dec 28 2021 10:35:49
%S A350377 1,5,8,10,11,12,14,21,23,24,27,63,64,72,90,99,144,176,184,340,366,393,
%T A350377 480,567,693,915,975,1046,1068,1084,1260,1410,1452,1830,1968,2268,
%U A350377 2490,2943,3087,3735,5284,5426,5637,5757,6015,6334,6393,6570,6582,8292,9836,10005
%N 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)).
%C A350377 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).
%F A350377 Numbers k such that A221490(k) = A344349(k).
%e A350377 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.
%e A350377   [1   2  3  4  5]
%e A350377   [6   7  8  9 10]
%e A350377   [11 12 13 14 15]
%e A350377   [16 17 18 19 20]
%e A350377   [21 22 23 24 25]
%t A350377 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 *)
%Y A350377 Cf. A000720 (pi), A221490, A344349, A350328.
%K A350377 nonn
%O A350377 1,2
%A A350377 _Wesley Ivan Hurt_, Dec 28 2021
%E A350377 More terms from _Amiram Eldar_, Dec 28 2021

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