A117530 - OEIS

%I #6 Apr 24 2015 09:20:01

%S 2,3,5,5,7,11,7,9,13,19,11,13,17,23,31,13,15,19,25,33,43,17,19,23,29,

%T 37,47,59,19,21,25,31,39,49,61,75,23,25,29,35,43,53,65,79,95,29,31,35,

%U 41,49,59,71,85,101,119,31,33,37,43,51,61,73,87,103,121,141,37,39,43,49,57

%N Triangle read by rows: T(n,k) = k^2 - k + prime(n), 1<=k<=n.

%C T(n,1) = A000040(k);

%C T(n,2) = A052147(k) for k>1;

%C A117531 gives number of primes in the n-th row;

%C if T(n,1) is a Lucky Number of Euler then A117531(n)=n, see A014556;

%C 1<k<n: T(n,k) = T(n,k-1) + T(n-1,k) - T(n-1,k-1).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LuckyNumberofEuler.html">Lucky Number of Euler</a>

%e T(5,k)=A048058(k)=A048059(k), 1<=k<=5: T(5,1)=A014556(4)=11;

%e T(7,k)=A007635(k), 1<=k<=7: T(7,1)=A014556(5)=17;

%e T(13,k)=A005846(k), 1<=k<=13: T(13,1)=A014556(6)=41.

%o (PARI) T(n,k) = k^2 - k + prime(n) \\ _Charles R Greathouse IV_, Apr 24 2015

%K nonn,tabl

%O 1,1

%A _Reinhard Zumkeller_, Mar 25 2006