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

1,2

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000341, A108018.

Cf. A010051, A000040.

Sequence in context: A195821 A372684 A208772 * A373654 A137576 A161329

Adjacent sequences: A071807 A071808 A071809 * A071811 A071812 A071813

Keyword

nonn,nice

Author

Robert G. Wilson v, Jun 06 2002

Extensions

More terms from Don Reble, Sep 07 2006

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

Status

approved