A071810 Number of subsets of the first n primes whose sum is a prime.

1, 3, 5, 7, 12, 20, 35, 65, 122, 237, 448, 846, 1629, 3157, 6159, 12052, 23484, 45731, 89394, 175742, 346214, 681850, 1344838, 2657654, 5253640, 10374991, 20471626, 40401929, 79871387, 158182899, 313402605, 620776215, 1228390086, 2430853648

Offset: 1

Author

Robert G. Wilson v, Jun 06 2002

Keywords

• nonn
• nice

Comments

a(n+1) < 2*a(n) fails for n = 1, 332 and other larger values of n. - Don Reble, Sep 07 2006

Here is one way to compute this sequence. Compute f_n(x) = Product_{k=1..n} 1+x^prime(k) = f_{n-1}(x) * (1+x^prime(n)). Then sum the coefficients of x^p in f_n(x) for p prime. You only need to look at primes <= the sum of the first n primes. - Franklin T. Adams-Watters, Sep 07 2006

Examples

			a(4) = 7 because, besides the original 4 primes, the other 3 subsets, {2,3}, {2,5} & {2,3,5,7} also sum to a prime.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from T. D. Noe)

Crossrefs

Cf. A000341, A108018.

Cf. A010051, A000040.

Programs

Haskell

import Data.List (subsequences)
a071810 = sum . map a010051' . map sum .
          tail . subsequences . flip take a000040_list
-- Reinhard Zumkeller, Dec 16 2013

Mathematica

Do[ Print[ Count[ PrimeQ[Plus @@@ Subsets[ Table[ Prime[i], {i, 1, n}]]], True]], {n, 1, 22}]
Table[Count[Total/@Subsets[Prime[Range[n]]],?PrimeQ],{n,20}] (* _Harvey P. Dale, Mar 03 2020 *)

Extensions

More terms from Don Reble, Sep 07 2006

Edited by N. J. A. Sloane, Sep 08 2006