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A088239
Triangle read by rows: T(n,k) is the number of primes not less than n-k and not greater than n+k, 0<=k<n.
0
0, 1, 2, 1, 2, 3, 0, 2, 3, 4, 1, 1, 3, 4, 4, 0, 2, 2, 3, 4, 5, 1, 1, 2, 2, 4, 5, 6, 0, 1, 1, 3, 3, 5, 6, 6, 0, 0, 2, 2, 4, 4, 5, 6, 7, 0, 1, 1, 3, 3, 4, 4, 6, 7, 8, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 8, 0, 2, 2, 2, 2, 4, 4, 6, 6, 7, 8, 9, 1, 1, 2, 2, 3, 3, 5, 5, 6, 6, 8, 9, 9, 0, 1, 1, 3, 3, 4, 4, 5, 5, 7, 7, 8, 9, 9
OFFSET
1,3
FORMULA
T(n,0) = A010051(n); T(n,n-1) = A000720(2*n-1).
EXAMPLE
Triangle begins:
0;
1, 2;
1, 2, 3;
0, 2, 3, 4;
1, 1, 3, 4, 4;
0, 2, 2, 3, 4, 5;
...
MATHEMATICA
T[n_, k_] := PrimePi[n+k] - PrimePi[n-k-1];
Table[T[n, k], {n, 1, 14}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Sep 18 2021 *)
CROSSREFS
Sequence in context: A141455 A292627 A113125 * A130070 A273516 A082501
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Nov 03 2003
STATUS
approved