

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
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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,n2) = A048448(n) for n>2;
T(n,n1) = 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



