A131424 Triangle read by rows: T(n,k) = prime(n) + prime(k) - 3, 1 <= k <= n.

1, 2, 3, 4, 5, 7, 6, 7, 9, 11, 10, 11, 13, 15, 19, 12, 13, 15, 17, 21, 23, 16, 17, 19, 21, 25, 27, 31, 18, 19, 21, 23, 27, 29, 33, 35, 22, 23, 25, 27, 31, 33, 37, 39, 43, 28, 29, 31, 33, 37, 39, 43, 45, 49, 55, 30, 31, 33, 35, 39, 41, 45, 47, 51, 57, 59

Offset: 1

Author

Gary W. Adamson, Jul 10 2007

Keywords

• nonn
• tabl

Comments

Left border = A006093, (primes - 1): (1, 2, 4, 6, 10, 12, ...). Right border = A131426 (2*primes - 3): (1, 3, 7, 11, 19, 23, 31, ...). Row sums = A131425: (1, 5, 16, 33, 68, 101, 156, ...).

Examples

			First few rows of the triangle are:
   1;
   2,  3;
   4,  5,  7;
   6,  7,  9, 11;
  10, 11, 13, 15, 19;
  12, 13, 15, 17, 21, 23;
  16, 17, 19, 21, 25, 27, 31;
  18, 19, 21, 23, 27, 29, 33, 35;
  22, 23, 25, 27, 31, 33, 37, 39, 43;
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Crossrefs

Row sums are A131425.

Cf. A127640, A131426, A006093, A000040.

Programs

Mathematica

T[n_,k_]:=Prime[n]+Prime[k]-3;Table[T[n,k],{n,11},{k,n}]//Flatten (* James C. McMahon, Feb 20 2025 *)

PARI

T(n,k) = if(k<=n, prime(n) + prime(k) - 3, 0) \\ Andrew Howroyd, Sep 01 2018

Formula

Equals (A000012 * A127640) + (A127640 * A000012) - 3*A000012 as infinite lower triangular matrices.

Extensions

Name clarified and terms a(56) and beyond from Andrew Howroyd, Sep 01 2018