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A117530 Triangle read by rows: T(n,k) = k^2 - k + prime(n), 1<=k<=n.

%I A117530 #14 Apr 19 2025 06:17:08
%S A117530 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 A117530 37,47,59,19,21,25,31,39,49,61,75,23,25,29,35,43,53,65,79,95,29,31,35,
%U A117530 41,49,59,71,85,101,119,31,33,37,43,51,61,73,87,103,121,141,37,39,43,49,57
%N A117530 Triangle read by rows: T(n,k) = k^2 - k + prime(n), 1<=k<=n.
%C A117530 A117531 gives the number of primes in the n-th row;
%C A117530 if T(n,1) is a Lucky Number of Euler then A117531(n)=n, see A014556.
%H A117530 Robert Price, <a href="/A117530/b117530.txt">Table of n, a(n) for n = 1..10011</a>
%H A117530 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%H A117530 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LuckyNumberofEuler.html">Lucky Number of Euler</a>
%F A117530 T(n,1) = A000040(k).
%F A117530 T(n,2) = A052147(k) for k>1.
%F A117530 For 1<k<n: T(n,k) = T(n,k-1) + T(n-1,k) - T(n-1,k-1).
%e A117530 T(5,k)=A048058(k)=A048059(k), 1<=k<=5: T(5,1)=A014556(4)=11;
%e A117530 T(7,k)=A007635(k), 1<=k<=7: T(7,1)=A014556(5)=17;
%e A117530 T(13,k)=A005846(k), 1<=k<=13: T(13,1)=A014556(6)=41.
%t A117530 Table[k^2 - k + Prime[n], {n, 141}, {k, n}] // Flatten (* _Robert Price_, Apr 19 2025 *)
%o A117530 (PARI) T(n,k) = k^2 - k + prime(n) \\ _Charles R Greathouse IV_, Apr 24 2015
%Y A117530 Cf. A005846, A007635, A014556, A048058, A048059, A117531.
%K A117530 nonn,tabl
%O A117530 1,1
%A A117530 _Reinhard Zumkeller_, Mar 25 2006