

A117530


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


6



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
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OFFSET

1,1


COMMENTS

T(n,1) = A000040(k);
T(n,2) = A052147(k) for k>1;
A117531 gives number of primes in the nth 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,k1) + T(n1,k)  T(n1,k1).


LINKS

Table of n, a(n) for n=1..71.
Eric Weisstein's World of Mathematics, PrimeGenerating 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



