A256015 Triangle read by rows: n-th row contains all distinct primes which are representable as the sum of some subset of the set of first n primes.

2, 2, 3, 5, 2, 3, 5, 7, 2, 3, 5, 7, 17, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67

Offset: 1

Author

Reinhard Zumkeller, Jun 01 2015

Keywords

• nonn
• tabf

Comments

A066028(n) = T(n,A108018(n)).

Examples

			.  1:  2 |
.  2:  2 3 | 5
.  3:  2 3 5 | 7
.  4:  2 3 5 7 | 17
.  5:  2 3 5 7 11 | 13  17  19  23
.  6:  2 3 5 7 11 13 | 17  19  23  29  31  41
.  7:  2 3 5 7 11 13 17 | 19  23  29  31  37  41  43  47  53
.  8:  2 3 5 7 11 13 17 19 | 23  29  31  37  41  43  47  53  59  61  67 .
		

Links

• Reinhard Zumkeller, Rows n = 1..25 of triangle, flattened

Crossrefs

Cf. A010051, A000040, A108018 (row lengths), A066028 (right edge).

Programs

Haskell

import Data.List (subsequences, nub, sort)
a256015 n k = a256015_tabf !! (n-1) !! (k-1)
a256015_row n = a256015_tabf !! (n-1)
a256015_tabf = map (sort . filter ((== 1) . a010051') . nub .
                map sum . tail . subsequences) (tail $ inits a000040_list)