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

1,1

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).

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Index entries for sequences related to Goldbach conjecture

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A366728 A256964 A046344 * A315849 A138890 A189082

Adjacent sequences: A116363 A116364 A116365 * A116367 A116368 A116369

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Feb 06 2006

Status

approved