OFFSET
1,1
COMMENTS
Define the auxiliary sequence 3, 2, 7, 5, 13, 11, 19, 17, 29, 23, 37, 31, 43,.. by b(n)=prime(n-1) if n is even and b(n) = prime(n+1) if n is odd. Then T(n,k) = b(n) *prime(k).
EXAMPLE
Triangle starts:
2* 3;
2* 2, 3* 2;
2* 7, 3* 7, 5* 7;
2* 5, 3* 5, 5* 5, 7* 5;
2*13, 3*13, 5*13, 7*13,11*13;
2*11, 3*11, 5*11, 7*11,11*11,13*11;
2*19, 3*19, 5*19, 7*19,11*19,13*19,17*19;
2*17, 3*17, 5*17, 7*17,11*17,13*17,17*17,19*17;
2*29, 3*29, 5*29, 7*29,11*29,13*29,17*29,19*29,23*29;
2*23, 3*23, 5*23, 7*23,11*23,13*23,17*23,19*23,23*23,29*23;
...
=
6;
4,6;
14,21,35;
10,15,25,35;
26,39,65,91,143;
22,33,55,77,121,143;
38,57,95,133,209,247,323;
34,51,85,119,187,221,289,323;
58,87,145,203,319,377,493,551,667;
46,69,115,161,253,299,391,437,529,667;
...
MATHEMATICA
T[n_, k_]:=(If[EvenQ[n], (Prime[n-1]), Prime[n+1]]) Prime[k]; Table[T[n, k], {n, 1, 15}, {k, 1, n}]//Flatten (* Vincenzo Librandi, Dec 28 2018 *)
PROG
(PARI) T(n, k) = if (n % 2, prime(n+1), prime(n-1))*prime(k); \\ Michel Marcus, Dec 28 2018
(Magma) /* As triangle */ [[(IsOdd(n) select NthPrime(n+1) else NthPrime(n-1))* NthPrime(k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 28 2018
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 10 2005
STATUS
approved