A143537 Triangle read by rows: T(n,k) = number of primes in the interval [k..n], n >= 1, 1 <= k <= n.

0, 1, 1, 2, 2, 1, 2, 2, 1, 0, 3, 3, 2, 1, 1, 3, 3, 2, 1, 1, 0, 4, 4, 3, 2, 2, 1, 1, 4, 4, 3, 2, 2, 1, 1, 0, 4, 4, 3, 2, 2, 1, 1, 0, 0, 4, 4, 3, 2, 2, 1, 1, 0, 0, 0, 5, 5, 4, 3, 3, 2, 2, 1, 1, 1, 1, 5, 5, 4, 3, 3, 2, 2, 1, 1, 1, 1, 0, 6, 6, 5, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1

Offset: 1

Author

Gary W. Adamson, Aug 23 2008

Keywords

• nonn
• tabl

Comments

Old name: triangle read by rows, A000012 * A143536, 1<=k<=n.

Examples

			Triangle T(n,k) begins:
n\k 1  2  3  4  5  6  7  8 ...
1:  0;
2:  1, 1;
3:  2, 2, 1;
4:  2, 2, 1, 0;
5:  3, 3, 2, 1, 1;
6:  3, 3, 2, 1, 1, 0;
7:  4, 4, 3, 2, 2, 1, 1;
8:  4, 4, 3, 2, 2, 1, 1, 0;
...
		

Crossrefs

Row sums are A034387.

Column k=1 gives A000720.

Main diagonal gives A010051.

T(2n,n) gives A035250.

Cf. A143536.

Formula

T(n,k) = pi(n) - pi(k-1), where pi = A000720. - Ilya Gutkovskiy, Mar 19 2020

Extensions

New name and corrected by Ilya Gutkovskiy, Mar 19 2020