A147815 - OEIS

%I #21 Oct 16 2024 21:25:51

%S 2,3,3,3,3,5,11,17,23,7,-1,-9,-17,-25,11,21,31,41,51,61,13,1,-11,-23,

%T -35,-47,-59,17,31,45,59,73,87,101,115,19,35,51,67,83,99,115,131,147,

%U 23,-13,-49,-85,-121,-157,-193,-229,-265,-301,29,69,109,149,189,229,269

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

%F t(n, k) = k*n*A036263(n) + A000040(n). - _M. F. Hasler_, Oct 15 2024

%e {2, 3},

%e {3, 3, 3},

%e {5, 11, 17, 23},

%e {7, -1, -9, -17, -25},

%e {11, 21, 31, 41, 51, 61},

%e {13, 1, -11, -23, -35, -47, -59},

%e {17, 31, 45, 59, 73, 87, 101, 115},

%e {19, 35, 51, 67, 83, 99, 115,131, 147},

%e {23, -13, -49, -85, -121, -157, -193, -229, -265, -301},

%e {29, 69, 109, 149, 189, 229, 269, 309, 349, 389, 429},

%e ...

%o (PARI) A147815(n,k)=k*n*(prime(n) - 2*prime(n+1) + prime(n+2)) + prime(n)

%o [[A147815(n,k) | k<-[0..n]] | n<-[1..9]]

%Y Cf. A036263 (2nd differences of primes).

%K sign,tabf,less

%O 1,1

%A _Roger L. Bagula_, Nov 13 2008

%E Edited by _M. F. Hasler_, Oct 15 2024