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

1,1

Comments

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

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

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

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

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

Links

Table of n, a(n) for n=1..71.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Eric Weisstein's World of Mathematics, Lucky Number of Euler

Example

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.

Prog

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

Crossrefs

Sequence in context: A156898 A084754 A120724 * A238256 A239277 A302445

Adjacent sequences: A117527 A117528 A117529 * A117531 A117532 A117533

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Mar 25 2006

Status

approved