A147815 Triangle t(n, k) = k*n*(prime(n+2) - 2*prime(n+1) + prime(n)) + prime(n), 0 <= k <= n = 1, 2, 3, ...

2, 3, 3, 3, 3, 5, 11, 17, 23, 7, -1, -9, -17, -25, 11, 21, 31, 41, 51, 61, 13, 1, -11, -23, -35, -47, -59, 17, 31, 45, 59, 73, 87, 101, 115, 19, 35, 51, 67, 83, 99, 115, 131, 147, 23, -13, -49, -85, -121, -157, -193, -229, -265, -301, 29, 69, 109, 149, 189, 229, 269

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Formula

t(n, k) = k*n*A036263(n) + A000040(n). - M. F. Hasler, Oct 15 2024

Example

{2, 3},
{3, 3, 3},
{5, 11, 17, 23},
{7, -1, -9, -17, -25},
{11, 21, 31, 41, 51, 61},
{13, 1, -11, -23, -35, -47, -59},
{17, 31, 45, 59, 73, 87, 101, 115},
{19, 35, 51, 67, 83, 99, 115,131, 147},
{23, -13, -49, -85, -121, -157, -193, -229, -265, -301},
{29, 69, 109, 149, 189, 229, 269, 309, 349, 389, 429},
...

Prog

(PARI) A147815(n, k)=k*n*(prime(n) - 2*prime(n+1) + prime(n+2)) + prime(n)
[[A147815(n, k) | k<-[0..n]] | n<-[1..9]]

Crossrefs

Cf. A036263 (2nd differences of primes).

Sequence in context: A129263 A035367 A042959 * A227246 A200924 A111913

Adjacent sequences: A147812 A147813 A147814 * A147816 A147817 A147818

Keyword

sign,tabf,less

Author

Roger L. Bagula, Nov 13 2008

Extensions

Edited by M. F. Hasler, Oct 15 2024

Status

approved