%I #15 Feb 05 2013 05:09:03

%S 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,

%T 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,

%U 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

%N 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.

%C 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

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

%H T. D. Noe, <a href="/A083415/b083415.txt">Rows n=1..100 of triangle, flattened</a>

%e {0}

%e {1, 1}

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

%e {2, 2, 1, 1}

%e {3, 1, 2, 2, 1}

%e {3, 2, 2, 2, 1, 1}

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

%o (Haskell)

%o a083415 n k = a083415_row n !! (k-1)

%o a083415_row n = f n a010051_list where

%o f 0 _ = []

%o f k chips = (sum chin) : f (k - 1) chips' where

%o (chin,chips') = splitAt n chips

%o a083415_tabl = map a083415_row [1..]

%o -- _Reinhard Zumkeller_, Jun 10 2012

%Y Cf. A083382, A083414, A092556, A092557.

%Y Cf. A139325.

%Y Cf. A010051.

%K nonn,tabl

%O 1,4

%A _N. J. A. Sloane_, following a suggestion of _Wouter Meeussen_, Jun 10 2003