A083415 Triangle read by rows: T(n,k) is defined as follows. Write the numbers from 1 to n^2 consecutively in n rows of length n; T(n,k) = number of primes in k-th row.

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

Offset: 1

Author

N. J. A. Sloane, following a suggestion of Wouter Meeussen, Jun 10 2003

Keywords

• nonn
• tabl

Comments

Sum(T(n,k): 1<=k<=n) = A038107(n); T(n,1)=A000720(n); T(n,2)=A060715(n) for n>1. - Reinhard Zumkeller, Jan 07 2004

Examples

			{0}
{1, 1}
{2, 1, 1} from / 1 2 3 / 4 5 6 / 7 8 9 /
{2, 2, 1, 1}
{3, 1, 2, 2, 1}
{3, 2, 2, 2, 1, 1}
		

References

• Paulo Ribenboim, "The Little Book Of Big Primes," Springer-Verlag, NY 1991, page 185.

Links

• T. D. Noe, Rows n=1..100 of triangle, flattened

Crossrefs

Cf. A083382, A083414, A092556, A092557.

Cf. A139325.

Cf. A010051.

Programs

Haskell

a083415 n k = a083415_row n !! (k-1)
a083415_row n = f n a010051_list where
   f 0 _     = []
   f k chips = (sum chin) : f (k - 1) chips' where
     (chin,chips') = splitAt n chips
a083415_tabl = map a083415_row [1..]
-- Reinhard Zumkeller, Jun 10 2012

Mathematica

Table[PrimePi[m n]-PrimePi[(m-1) n], {n, 17}, {m, n}]