A116366 Triangle read by rows: even numbers as sums of two odd primes.

6, 8, 10, 10, 12, 14, 14, 16, 18, 22, 16, 18, 20, 24, 26, 20, 22, 24, 28, 30, 34, 22, 24, 26, 30, 32, 36, 38, 26, 28, 30, 34, 36, 40, 42, 46, 32, 34, 36, 40, 42, 46, 48, 52, 58, 34, 36, 38, 42, 44, 48, 50, 54, 60, 62, 40, 42, 44, 48, 50, 54, 56, 60, 66, 68, 74, 44, 46, 48, 52, 54, 58, 60, 64, 70, 72, 78, 82

Offset: 1

Author

Reinhard Zumkeller, Feb 06 2006

Keywords

• nonn
• tabl

Comments

T(n,k) = 2*A065305(n,k) = A065342(n+1,k+1);

Row sums give A116367; central terms give A116368;

T(n,1) = A113935(n+1);

T(n,n-2) = A048448(n) for n>2;

T(n,n-1) = A001043(n) for n>1;

T(n,n) = A001747(n+2) = A100484(n+1).

Examples

			Triangle begins:
  6;
  8,  10;
  10, 12, 14;
  14, 16, 18, 22;
  16, 18, 20, 24, 26;
  20, 22, 24, 28, 30, 34;
  22, 24, 26, 30, 32, 36, 38;
  26, 28, 30, 34, 36, 40, 42, 46;
  32, 34, 36, 40, 42, 46, 48, 52, 58;
  34, 36, 38, 42, 44, 48, 50, 54, 60, 62;
  40, 42, 44, 48, 50, 54, 56, 60, 66, 68, 74;
  44, 46, 48, 52, 54, 58, 60, 64, 70, 72, 78, 82; etc. - _Bruno Berselli_, Aug 16 2013
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A001043, A001747, A048448, A065305, A065342, A100484, A113935, A116367, A116368.

Programs

Magma

[NthPrime(n+1)+NthPrime(k+1): k in [1..n], n in [1..15]]; // Bruno Berselli, Aug 16 2013

Mathematica

Table[Prime[n+1] + Prime[k+1], {n,1,12}, {k,1,n}]//Flatten (* G. C. Greubel, May 12 2019 *)

PARI

{T(n,k) = prime(n+1) + prime(k+1)}; \\ G. C. Greubel, May 12 2019

Sage

[[nth_prime(n+1) + nth_prime(k+1) for k in (1..n)] for n in (1..12)] # G. C. Greubel, May 12 2019

Formula

T(n,k) = prime(n+1) + prime(k+1), 1 <= k <= n.