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 A342695 a(n) is the number of primes in an n X n square array that do not appear on its border, with the elements of the square array being the numbers from 1..n^2, listed in increasing order by rows. 0
 0, 0, 1, 2, 4, 4, 8, 10, 14, 15, 21, 21, 27, 31, 36, 42, 48, 46, 58, 61, 68, 73, 83, 83, 96, 100, 110, 114, 127, 123, 144, 146, 157, 165, 175, 179, 201, 201, 212, 221, 241, 235, 258, 265, 275, 282, 303, 301, 328, 330, 346, 351, 381, 377, 403, 406, 427, 433, 455, 452, 486, 493 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..62. FORMULA a(n) = pi(n*(n-1)) - pi(n) - Sum_{k=1..n-2} (pi(n*k+1) - pi(n*k)). 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 0 1 2 4 ------------------------------------------------------------------------ primes {} {} {5} {7,11} {7,13,17,19} ------------------------------------------------------------------------ MATHEMATICA Table[PrimePi[n*(n - 1)] - PrimePi[n] - Sum[PrimePi[n*k + 1] - PrimePi[n*k], {k, n - 2}], {n, 100}] CROSSREFS Cf. A000720 (pi), A038107, A221490, A344316 (on border), A344349. Sequence in context: A213064 A076466 A073117 * A039879 A125204 A241386 Adjacent sequences: A342692 A342693 A342694 * A342696 A342697 A342698 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 18 2021 STATUS approved

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Last modified December 1 17:35 EST 2023. Contains 367500 sequences. (Running on oeis4.)