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A116366 Triangle read by rows: even numbers as sums of two odd primes. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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: A001743 A256964 A046344 * A315849 A138890 A189082

Adjacent sequences:  A116363 A116364 A116365 * A116367 A116368 A116369

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Feb 06 2006

STATUS

approved

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Last modified July 11 01:46 EDT 2020. Contains 335600 sequences. (Running on oeis4.)