A289108 Triangle read by rows: T(n,k) = (k + 1)*prime(n) + k for n > 0, 0 <= k <= n, and with T(0,0) = 1.

1, 2, 5, 3, 7, 11, 5, 11, 17, 23, 7, 15, 23, 31, 39, 11, 23, 35, 47, 59, 71, 13, 27, 41, 55, 69, 83, 97, 17, 35, 53, 71, 89, 107, 125, 143, 19, 39, 59, 79, 99, 119, 139, 159, 179, 23, 47, 71, 95, 119, 143, 167, 191, 215, 239, 29, 59, 89, 119, 149, 179, 209, 239, 269, 299, 329

Offset: 0

Author

Vincenzo Librandi, Sep 02 2017

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   2,   5;
   3,   7,  11;
   5,  11,  17,  23;
   7,  15,  23,  31,  39;
  11,  23,  35,  47,  59,  71;
  13,  27,  41,  55,  69,  83,  97;
  17,  35,  53,  71,  89, 107, 125, 143;
  19,  39,  59,  79,  99, 119, 139, 159, 179;
  23,  47,  71,  95, 119, 143, 167, 191, 215, 239;
  ...
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A000040, A008578, A072055.

Programs

Magma

/* As triangle (here NthPrime(0)=1) */ [[(k+1)*NthPrime(n)+k: k in [0..n]]: n in [0.. 15]];

Mathematica

Join[{1}, T[n_,k_] := (k + 1) Prime[n] + k; Table[T[n, k], {n, 10}, {k, 0, n}]//Flatten]

SageMath

def A289108(n,k): return 1 if n==0 else (k+1)*nth_prime(n) +k
flatten([[A289108(n,k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Aug 04 2024

Extensions

Definition corrected by Bruno Berselli, Sep 06 2017