A066028 -id:A066028 - cp's OEIS frontend

A108018 a(n) = the number of primes representable as the sum of some subset of the set of first n primes.

1, 3, 4, 5, 9, 12, 16, 19, 25, 31, 37, 43, 51, 59, 66, 75, 84, 95, 103, 115, 127, 137, 150, 162, 177, 191, 205, 218, 233, 250, 267, 282, 299, 319, 338, 359, 376, 399, 421, 440, 461, 481, 508, 531, 556, 578, 602, 629, 653, 683, 707, 737, 765, 793, 824, 853, 883

Offset: 1

Max Alekseyev, Sep 08 2006

nonn

a(n) = length of n-th row in A256015; A066028(n) = A256015(n,a(n)). - Reinhard Zumkeller, Jun 01 2015

Alois P. Heinz, Table of n, a(n) for n = 1..500

Cf. A071810 (same count but with multiplicities).
Cf. A010051, A000040.
Cf. A066028, A256015.

import Data.List (subsequences, nub)
a108018 = sum . map a010051' . nub . map sum .
          tail . subsequences . flip take a000040_list
-- Reinhard Zumkeller, Dec 16 2013

(* This program is not suitable to compute a large number of terms. *)
a[n_] := a[n] = Select[Total /@ Subsets[Table[Prime[i], {i, 1, n}]], PrimeQ] // Union // Length;
Table[Print[n, " ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 12 2019 *)

More terms from Alois P. Heinz, Oct 24 2015

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.

Original entry on oeis.org

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

Reinhard Zumkeller, Jun 01 2015

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

			.  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 .

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

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

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)

cp's OEIS Frontend

A108018 a(n) = the number of primes representable as the sum of some subset of the set of first n primes.

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