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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.

%I A083415 #15 Feb 05 2013 05:09:03
%S A083415 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 A083415 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 A083415 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 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.
%C A083415 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 A083415 Paulo Ribenboim, "The Little Book Of Big Primes," Springer-Verlag, NY 1991, page 185.
%H A083415 T. D. Noe, <a href="/A083415/b083415.txt">Rows n=1..100 of triangle, flattened</a>
%e A083415 {0}
%e A083415 {1, 1}
%e A083415 {2, 1, 1} from / 1 2 3 / 4 5 6 / 7 8 9 /
%e A083415 {2, 2, 1, 1}
%e A083415 {3, 1, 2, 2, 1}
%e A083415 {3, 2, 2, 2, 1, 1}
%t A083415 Table[PrimePi[m n]-PrimePi[(m-1) n], {n, 17}, {m, n}]
%o A083415 (Haskell)
%o A083415 a083415 n k = a083415_row n !! (k-1)
%o A083415 a083415_row n = f n a010051_list where
%o A083415    f 0 _     = []
%o A083415    f k chips = (sum chin) : f (k - 1) chips' where
%o A083415      (chin,chips') = splitAt n chips
%o A083415 a083415_tabl = map a083415_row [1..]
%o A083415 -- _Reinhard Zumkeller_, Jun 10 2012
%Y A083415 Cf. A083382, A083414, A092556, A092557.
%Y A083415 Cf. A139325.
%Y A083415 Cf. A010051.
%K A083415 nonn,tabl
%O A083415 1,4
%A A083415 _N. J. A. Sloane_, following a suggestion of _Wouter Meeussen_, Jun 10 2003