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

Author

Max Alekseyev, Sep 08 2006

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A071810 (same count but with multiplicities).

Cf. A010051, A000040.

Cf. A066028, A256015.

Programs

Haskell

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

Mathematica

(* 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 *)

Extensions

More terms from Alois P. Heinz, Oct 24 2015