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A221490
Number of primes of the form k*n + k - n, 1 <= k <= n.
10
0, 0, 1, 1, 3, 1, 2, 2, 5, 3, 6, 3, 5, 4, 4, 3, 9, 2, 6, 5, 8, 4, 9, 4, 9, 7, 10, 4, 17, 3, 10, 9, 11, 9, 15, 4, 9, 10, 13, 5, 20, 7, 11, 10, 16, 8, 19, 6, 18, 12, 17, 5, 23, 9, 18, 9, 15, 8, 26, 7, 15, 12, 16, 13, 29, 8, 18, 13, 26, 9, 25, 10, 19, 18, 16
OFFSET
1,5
COMMENTS
Number of primes in n-th row of the triangle in A209297.
Number of primes along the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see square arrays in example). - Wesley Ivan Hurt, May 15 2021
LINKS
FORMULA
a(n) = Sum_{k=1..n} A010051(A209297(n,k)).
a(n) = Sum_{k=1..n} c(n*(k-1)+k), where c is the prime characteristic. - Wesley Ivan Hurt, May 15 2021
EXAMPLE
Row 10 of A209297 = [1,12,23,34,45,56,67,78,89,100] containing three primes: [23,67,89], therefore a(10) = 3;
row 11 of A209297 = [1,13,25,37,49,61,73,85,97,109,121] containing six primes: [13,37,61,73,97,109], therefore a(11) = 6.
From Wesley Ivan Hurt, May 15 2021: (Start)
[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 1 3
------------------------------------------------------------------------
(End)
MATHEMATICA
Count[#, _?PrimeQ]&/@Table[k*n+k-n, {n, 75}, {k, n}] (* Harvey P. Dale, Apr 03 2015 *)
PROG
(Haskell)
a221490 n = sum [a010051 (k*n + k - n) | k <- [1..n]]
(PARI) a(n) = sum(k=1, n, isprime(k*n + k - n)); \\ Michel Marcus, Jan 26 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 19 2013
STATUS
approved