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

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, 37, 47, 59, 19, 21, 25, 31, 39, 49, 61, 75, 23, 25, 29, 35, 43, 53, 65, 79, 95, 29, 31, 35, 41, 49, 59, 71, 85, 101, 119, 31, 33, 37, 43, 51, 61, 73, 87, 103, 121, 141, 37, 39, 43, 49, 57

Offset: 1

Author

Reinhard Zumkeller, Mar 25 2006

Keywords

• nonn
• tabl

Comments

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

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

Examples

			T(5,k)=A048058(k)=A048059(k), 1<=k<=5: T(5,1)=A014556(4)=11;
T(7,k)=A007635(k), 1<=k<=7: T(7,1)=A014556(5)=17;
T(13,k)=A005846(k), 1<=k<=13: T(13,1)=A014556(6)=41.
		

Links

• Robert Price, Table of n, a(n) for n = 1..10011
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
• Eric Weisstein's World of Mathematics, Lucky Number of Euler

Crossrefs

Cf. A005846, A007635, A014556, A048058, A048059, A117531.

Programs

Mathematica

Table[k^2 - k + Prime[n], {n, 141}, {k, n}] // Flatten (* Robert Price, Apr 19 2025 *)

PARI

T(n,k) = k^2 - k + prime(n) \\ Charles R Greathouse IV, Apr 24 2015

Formula

T(n,1) = A000040(k).

T(n,2) = A052147(k) for k>1.

For 1

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