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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
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).
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
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Feb 06 2006
STATUS
approved