A065342 Triangle of sum of two primes: prime(n)+prime(k) with n >= k >= 1.

4, 5, 6, 7, 8, 10, 9, 10, 12, 14, 13, 14, 16, 18, 22, 15, 16, 18, 20, 24, 26, 19, 20, 22, 24, 28, 30, 34, 21, 22, 24, 26, 30, 32, 36, 38, 25, 26, 28, 30, 34, 36, 40, 42, 46, 31, 32, 34, 36, 40, 42, 46, 48, 52, 58, 33, 34, 36, 38, 42, 44, 48, 50, 54, 60, 62, 39, 40, 42, 44, 48

Offset: 1

Author

Henry Bottomley, Oct 30 2001

Keywords

• nonn
• tabl

Examples

			Sequence starts 2+2; 3+2, 3+3; 5+2, 5+3, 5+5; etc. i.e. 4; 5,6; 7,8,10; ...
Triangle begins:
   4;
   5,  6;
   7,  8, 10;
   9, 10, 12, 14;
  13, 14, 16, 18, 22;
  ...
		

Links

• Reinhard Zumkeller, First 125 rows of triangle, flattened
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A052147 (left edge), A100484 (right edge), A000040.

Cf. A087112.

Cf. A065305.

Programs

Haskell

import Data.List (inits)
a065342 n k = a065342_tabl !! (n-1) !! (k-1)
a065342_row n = a065342_tabl !! (n-1)
a065342_tabl = zipWith (map . (+)) a000040_list $ tail $ inits a000040_list
-- Reinhard Zumkeller, Aug 02 2015, Jan 30 2012

PARI

row(n) = vector(n, k, prime(n)+prime(k)); \\ Michel Marcus, Sep 10 2021

Formula

T(n, k) = 2*A065305(n, k) [but note different offset].